Chat Index	Date	Time Start Typing	Time of Posting	137	Jason	qwertyuiop	davidcyl	azemel	Cynthia	jsarmi	nan	ssjnish	tutor	Gerry	hcrussel	Refers to
1	05/09/2006		18:15:57					joins the room
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4	05/09/2006		18:24:15	joins the room
5	05/09/2006	18:24:23	18:24:26					hey folks!
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6	05/09/2006	18:24:36	18:24:39					is everyone here?
	05/09/2006		18:24:41				[davidcyl created a rectangle ]
7	05/09/2006	18:24:41	18:24:42		i guess so
8	05/09/2006	18:24:43	18:24:44				yeaqh
9	05/09/2006	18:24:44	18:24:45	YA.
10	05/09/2006	18:24:45	18:24:46		4 people
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11	05/09/2006	18:24:50	18:24:52					great!
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12	05/09/2006	18:24:54	18:25:03					be sure to click on the view topic button
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13	05/09/2006	18:25:08	18:25:18					up at the top of the vmt screen
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14	05/09/2006	18:25:20	18:25:22				137 stop
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15	05/09/2006	18:25:29	18:25:29	Oops.
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16	05/09/2006	18:25:36	18:25:37				np
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17	05/09/2006	18:25:36	18:25:44		ooh we just did this in math class about a week ago! :-)
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18	05/09/2006	18:25:45	18:25:54					if you have any questions, just ask
19	05/09/2006	18:25:49	18:25:55		well, not the exact thing, but sequences and series
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20	05/09/2006	18:26:02	18:26:03		anyhow
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21	05/09/2006	18:26:08	18:26:21		so do we see how the number of sticks grows in a sequence?
22	05/09/2006	18:26:21	18:26:25				ok i've drawn n=4,5,6
23	05/09/2006	18:26:23	18:26:29		4(+6) = 10
24	05/09/2006	18:26:32	18:26:36		10(+8) = 18
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25	05/09/2006	18:26:37	18:26:48		i'm guessing 18(+10) = 28 for the next one, according to this pattern
	05/09/2006	18:26:58	18:27:10				[davidcyl has fully erased the chat message]
	05/09/2006	18:27:12	18:27:22		[Jason has fully erased the chat message]
26	05/09/2006	18:27:13	18:27:32				the nth pattern has n more squares than the (n-1)th pattern
	05/09/2006	18:27:30	18:27:47	[137 has fully erased the chat message]
	05/09/2006	18:27:47	18:27:52	[137 has fully erased the chat message]
27	05/09/2006	18:27:37	18:27:55				basically it's 1+2+..+(n-1)+n for the number of squares in the nth pattern
	05/09/2006	18:27:57	18:27:57	[137 has fully erased the chat message]
28	05/09/2006	18:28:02	18:28:16	so n(n+1)/2
29	05/09/2006	18:27:56	18:28:24				and we can use the gaussian sum to determine the sum: n(1+n)/2
30	05/09/2006	18:28:27	18:28:36				137 got it
31	05/09/2006	18:28:23	18:28:43	and 2(1+2+3...n-1) overlaps
32	05/09/2006	18:28:44	18:29:05	so n(n+1)/2-n(n-1)/2?
33	05/09/2006	18:29:26	18:29:31				well to find the number of sticks:
34	05/09/2006	18:29:31	18:29:39				let's look on the board
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35	05/09/2006	18:29:44	18:29:54		should we use a recursive or explicit definition for it
	05/09/2006		18:29:55				[davidcyl created a scribble ]
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	05/09/2006	18:30:11	18:30:11				[davidcyl has fully erased the chat message]
36	05/09/2006	18:30:12	18:30:20				i don't think we need recursion									[1] Reference to message No. 35 (Text: should we use a recursive or explicit definition for it )
37	05/09/2006	18:30:21	18:30:33				it's simpler to express it as 1+2+...+n
38	05/09/2006	18:30:46	18:30:50		would that be the number of sticks>
39	05/09/2006	18:30:38	18:30:51				anyway, when n=4, there's 1+2+3+4+4 horizontal sticks
	05/09/2006	18:30:51	18:30:54		[Jason has fully erased the chat message]
40	05/09/2006	18:30:55	18:31:03				and 1+2+3+4+4 vertical sticks
41	05/09/2006	18:31:04	18:31:06		let's see
42	05/09/2006	18:31:06	18:31:08		when n=2
	05/09/2006	18:31:08	18:31:17		[Jason has fully erased the chat message]
	05/09/2006	18:31:09	18:31:18				[davidcyl has fully erased the chat message]
43	05/09/2006	18:31:18	18:31:21	then we have 5.
44	05/09/2006	18:31:21	18:31:23				no, squares
	05/09/2006	18:31:18	18:31:25		[Jason has fully erased the chat message]
	05/09/2006	18:31:27	18:31:35		[Jason has fully erased the chat message]
45	05/09/2006	18:31:32	18:31:37				sorry i wasn't clear
46	05/09/2006	18:31:38	18:31:41	5*2=10.
	05/09/2006	18:31:43	18:31:43	[137 has fully erased the chat message]
47	05/09/2006	18:31:44	18:31:45	?
48	05/09/2006	18:31:51	18:31:54		ooh
	05/09/2006	18:31:41	18:32:00				[davidcyl has fully erased the chat message]
49	05/09/2006	18:31:59	18:32:02		well could you just use like
50	05/09/2006	18:32:07	18:32:20	n(n+2)?
51	05/09/2006	18:32:01	18:32:21				137: i'm separating the sticks into vertical and horizontal sticks
52	05/09/2006	18:32:24	18:32:25	oops.
53	05/09/2006	18:32:06	18:32:28		# sticks = N*(3+N)
	05/09/2006	18:32:26	18:32:30	[137 has fully erased the chat message]
54	05/09/2006	18:32:26	18:32:30				wait what are you working on?
55	05/09/2006	18:32:30	18:32:32		wait lemme check
56	05/09/2006	18:32:33	18:32:35				(to 137)
57	05/09/2006	18:32:42	18:32:46	Great. Confused.
58	05/09/2006	18:32:56	18:33:03		137 are you talking about # sticks or squares
	05/09/2006	18:32:48	18:33:07	[137 has fully erased the chat message]
59	05/09/2006	18:33:07	18:33:09	Sticks.
60	05/09/2006	18:33:17	18:33:18		ok
61	05/09/2006	18:32:47	18:33:21				i would think it's 2(n(1+n)/2) + n + n
62	05/09/2006	18:33:18	18:33:23		well i think my formula works
63	05/09/2006	18:33:29	18:33:33		provided that you have a value for N
	05/09/2006		18:33:40	[137 created a line ]
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64	05/09/2006	18:33:21	18:33:57				because it's basically (1+..+n + n) + (1 + .. + n + n)
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	05/09/2006		18:34:11		[Jason created a textbox ]
65	05/09/2006	18:34:10	18:34:12				checking
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66	05/09/2006		18:34:25									joins the room
67	05/09/2006	18:34:30	18:34:33		well hello nish
68	05/09/2006	18:34:38	18:34:42					welcom nish
69	05/09/2006	18:34:37	18:34:47		click on "view topic" near the top-center to see the problems
70	05/09/2006	18:34:56	18:34:57									welcome nish
71	05/09/2006	18:34:44	18:34:57					do you guys want to bring nish up to speed?
72	05/09/2006	18:34:33	18:35:03				this simplifies to n(1+n) + 2n, or n(3+n)									[1] Reference to message No. 61 (Text: i would think it's 2(n(1+n)/2) + n + n )
73	05/09/2006	18:35:05	18:35:09				so jason, you're right
74	05/09/2006	18:35:14	18:35:16		:-)
75	05/09/2006	18:35:30	18:35:36		so now onto a formula for the total number of squares
76	05/09/2006	18:35:36	18:35:42				ok let's complete the table
77	05/09/2006	18:35:39	18:35:46		if you take the change in the change of the number of squares, it's constant
	05/09/2006	18:35:46	18:35:47				[davidcyl has fully erased the chat message]
78	05/09/2006	18:36:07	18:36:10	Didn't we do that?												[1] Reference to message No. 75 (Text: so now onto a formula for the total number of squares )
	05/09/2006	18:36:12	18:36:14	[137 has fully erased the chat message]
	05/09/2006	18:35:48	18:36:14				[davidcyl has fully erased the chat message]
79	05/09/2006	18:36:14	18:36:19				yes
	05/09/2006	18:36:20	18:36:21		[Jason has fully erased the chat message]
80	05/09/2006	18:36:22	18:36:27		oh, sorry i guess i must've not caught that
81	05/09/2006	18:36:25	18:36:33				look up									[1] Reference to message No. 29 (Text: and we can use the gaussian sum to determine the sum: n(1+n)/2 )
82	05/09/2006	18:36:27	18:36:33		could someone post it in a text box on the whiteboard
83	05/09/2006	18:36:38	18:36:38				sure
84	05/09/2006	18:36:27	18:36:40					be sure that SSJNISH is up to speed folks
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85	05/09/2006	18:36:48	18:36:53					are you following ssjnish?
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86	05/09/2006	18:37:08	18:37:16		alright, so that formula's for sure right?
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87	05/09/2006	18:37:23	18:37:24	YA.
	05/09/2006	18:37:25	18:37:26	[137 has fully erased the chat message]
	05/09/2006	18:37:27	18:37:28	[137 has fully erased the chat message]
88	05/09/2006	18:37:27	18:37:33		yeah, sorry for moving the box around a little											[1] Reference to message No. 86 (Text: alright, so that formula's for sure right? )
89	05/09/2006	18:37:16	18:37:33				ssjnish, press the load messages button
90	05/09/2006	18:37:31	18:37:35	Ya.
91	05/09/2006	18:37:35	18:37:48				it's above this chat box, like 2 arrows in a circle
92	05/09/2006	18:37:44	18:37:50		it's the "reload"-like icon at the top of this box											[1] Reference to message No. 89 (Text: ssjnish, press the load messages button )
93	05/09/2006	18:37:52	18:37:53		yeah
94	05/09/2006	18:37:56	18:38:00					thanks davidcyl								[1] Reference to message No. 91 (Text: it's above this chat box, like 2 arrows in a circle )
95	05/09/2006	18:38:09	18:38:09									ok
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	05/09/2006		18:38:23	[137 changed layout ]
96	05/09/2006	18:37:56	18:38:30				basically, we've figured out that the number of squares in the nth pattern is 1 + 2 + ... + n
	05/09/2006		18:38:31		END:TextEditing
	05/09/2006		18:38:31		[Jason changed the text to: Formula for total # of squares: n(1+n)/2 ]
97	05/09/2006	18:38:28	18:38:33	It was blinding.
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	05/09/2006		18:39:04	[137 moved some object/s ]
98	05/09/2006	18:38:54	18:39:26				then, to find the number of sticks, I divided the figure into "vertical sticks" (|) and "horizontal sticks" (--)
99	05/09/2006	18:39:38	18:39:41		the formulas are on the Whiteboard
100	05/09/2006	18:39:44	18:39:56					don't forget to post your ideas to the wiki when you think it's time!
101	05/09/2006	18:39:36	18:40:15				the number of vertical sticks is (1 + 2 + 3 + ... + n)+ n, and the number of horizontal sticks is the same
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	05/09/2006		18:40:17	[137 resized some objects ]
102	05/09/2006	18:40:18	18:40:18				ok									[1] Reference to message No. 100 (Text: don't forget to post your ideas to the wiki when you think it's time! )
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103	05/09/2006	18:41:11	18:41:30		i'm writing our formulas in summation notation since apparently that's more "formal"
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104	05/09/2006	18:42:26	18:42:31		thats supposed to be an infinity symbol											[1] Reference to whiteboard (whiteboardDoc)
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	05/09/2006		18:42:51	START:TextEditing
105	05/09/2006	18:42:47	18:42:54				we need to write this on the wiki though
	05/09/2006		18:42:58	END:TextEditing
106	05/09/2006	18:42:58	18:42:58		oh yeah
107	05/09/2006	18:42:59	18:43:06		should we designate one person to do that or should we all do something
108	05/09/2006	18:43:08	18:43:09		on it
109	05/09/2006	18:43:17	18:43:20				i'm writing it up
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	05/09/2006		18:43:22		[Jason created a textbox ]
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110	05/09/2006	18:43:23	18:43:31				should we use the summation there?
111	05/09/2006	18:43:31	18:43:32		great
112	05/09/2006	18:43:33	18:43:36		for the formulas, shure
113	05/09/2006	18:43:37	18:43:37		sure*
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	05/09/2006		18:43:39				[davidcyl changed the text to: n ]
114	05/09/2006	18:43:38	18:43:44		do you know how to do that?
115	05/09/2006	18:43:47	18:43:47				yeah
116	05/09/2006	18:43:51	18:43:53		great
117	05/09/2006	18:44:01	18:44:04				i think you meant n									[1] Reference to whiteboard (EllipseStuff-1147218279687-8041650)
118	05/09/2006	18:44:09	18:44:09		yeah
119	05/09/2006	18:44:12	18:44:14				wait a second
120	05/09/2006	18:44:10	18:44:16		i started writing but then somehow it got erased
121	05/09/2006	18:44:16	18:44:17		oh well
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	05/09/2006		18:44:20				[davidcyl changed the text to: k ]
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	05/09/2006		18:44:22				[davidcyl changed the text to: k=1 ]
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122	05/09/2006	18:44:13	18:44:28	Erm... Where's the wiki?
	05/09/2006		18:44:30				[davidcyl copied some object/s ]
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	05/09/2006		18:44:35				START:TextEditing
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	05/09/2006		18:44:38				[davidcyl changed the text to: n ]
123	05/09/2006	18:44:38	18:44:39		http://mathforum.org/wiki/VMTStudents/?PatternsOfTheSticks
	05/09/2006	18:44:43	18:44:44		[Jason has fully erased the chat message]
	05/09/2006		18:44:44				[davidcyl moved some object/s ]
124	05/09/2006	18:44:44	18:44:50		or just click View Topic --> link to Wiki at end
125	05/09/2006	18:44:50	18:44:50													[1] Reference to whiteboard (whiteboardDoc)
126	05/09/2006	18:44:28	18:45:11									just to clarify sumthing, i am not overwhelmingly good at math as u guys seem to be, so it may take me more time than u guys to understand sumthing..
	05/09/2006	18:45:10	18:45:13		[Jason has fully erased the chat message]
127	05/09/2006	18:45:35	18:45:44					can you tell us what's puzzling you?
	05/09/2006	18:45:51	18:45:55									[ssjnish has fully erased the chat message]
128	05/09/2006	18:45:39	18:46:07		are we allowed to post images on the wiki? I could just download TeX real quick and get the summation notation in a small graphic
129	05/09/2006	18:46:04	18:46:12									the derivation of the number of squares
130	05/09/2006	18:46:20	18:46:21		oh
	05/09/2006	18:46:22	18:46:26		[Jason has fully erased the chat message]
131	05/09/2006	18:46:27	18:46:31		so you see in the list a column for "N"
	05/09/2006	18:46:22	18:46:43	[137 has fully erased the chat message]
132	05/09/2006	18:46:40	18:46:50		when n=1, we have 1 square; for n=2, 3; and for n=3, 6
	05/09/2006	18:46:43	18:46:55	[137 has fully erased the chat message]
133	05/09/2006	18:46:52	18:47:00		we came up with a formula to find the total number of squares for any number N
	05/09/2006	18:47:02	18:47:06		[Jason has fully erased the chat message]
134	05/09/2006	18:47:07	18:47:16		the purpose of the formula is so that you don't have to draw out the squares and count them
	05/09/2006	18:47:17	18:47:22		[Jason has fully erased the chat message]
135	05/09/2006	18:47:37	18:47:39									um yes
136	05/09/2006	18:47:41	18:47:41									i know
137	05/09/2006	18:47:42	18:47:51									but how did u get that formula
	05/09/2006	18:47:29	18:47:59		[Jason has fully erased the chat message]
138	05/09/2006	18:48:00	18:48:00		oh											[1] Reference to whiteboard (whiteboardDoc)
139	05/09/2006	18:48:09	18:48:11					i believe so								[1] Reference to message No. 128 (Text: are we allowed to post images on the wiki? I could just download TeX real quick and get the summation notation in a small graphic )
140	05/09/2006	18:48:05	18:48:12		uh, basically you try to find a pattern in the total number of squares first
	05/09/2006	18:48:25	18:48:36		[Jason has fully erased the chat message]
141	05/09/2006	18:48:36	18:48:47		we found a formula for that which we'll post on the wiki
	05/09/2006		18:48:59									[ssjnish moved some object/s ]
142	05/09/2006	18:48:39	18:49:00				if you look at the patterns row by row, it's 1 + 2 + 3 + 4 + however many rows there are
	05/09/2006	18:49:16	18:49:17		[Jason has fully erased the chat message]
143	05/09/2006	18:49:11	18:49:24				so for the nth pattern, we can say there are 1 + ... + n squares
144	05/09/2006	18:49:18	18:49:27		if N rows: 1+2+3+...N
	05/09/2006	18:49:37	18:49:43		[Jason has fully erased the chat message]
145	05/09/2006	18:49:44	18:49:57		so then we incorporated the formula for finding the sum of an arithmetic series
146	05/09/2006	18:49:29	18:50:12				there's a formula for finding the sum of consecutive integers, which (when starting from 1) is: n(n+1)/2
	05/09/2006	18:50:01	18:50:14		[Jason has fully erased the chat message]
	05/09/2006	18:50:13	18:50:16				[davidcyl has fully erased the chat message]
147	05/09/2006	18:49:56	18:50:17	so you use gaussian sum to get n(n+1)/2												[1] Reference to message No. 123 (Text: http://mathforum.org/wiki/VMTStudents/?PatternsOfTheSticks )
148	05/09/2006	18:50:23	18:50:25		that's it											[1] Reference to message No. 146 (Text: there's a formula for finding the sum of consecutive integers, which (when starting from 1) is: n(n+1)/2 )
149	05/09/2006	18:50:17	18:50:35				and as Jason said, it works for arithmetic sequences in general
150	05/09/2006	18:50:36	18:50:51									hmm...
151	05/09/2006	18:50:54	18:50:56									isee
152	05/09/2006	18:50:46	18:50:56		on a side note, you'll be doing stuff of similar sort next year in Algebra II
153	05/09/2006	18:50:57	18:51:01									thanks
154	05/09/2006	18:51:05	18:51:11				ok so let's finish the problem
155	05/09/2006	18:51:12	18:51:13				#2:
	05/09/2006	18:51:14	18:51:15				[davidcyl has fully erased the chat message]
156	05/09/2006	18:51:20	18:51:20				Fill in the cells of the table for sticks and squares in rows N=4, N=5, and N=6. Once you agree on the value of a row, post it on the VMT Wiki
	05/09/2006	18:51:26	18:51:29				[davidcyl has fully erased the chat message]
	05/09/2006	18:51:28	18:51:42		[Jason has fully erased the chat message]
157	05/09/2006	18:51:29	18:51:48				so when there's 4 rows, there should be 10 squares and 28 sticks
	05/09/2006	18:51:49	18:51:50				[davidcyl has fully erased the chat message]
158	05/09/2006	18:51:50	18:51:52				by our formulas
159	05/09/2006		18:52:03
160	05/09/2006	18:51:54	18:52:03				and we could count									[1] Reference to whiteboard (whiteboardDoc)
161	05/09/2006	18:52:10	18:52:11	Oops.
162	05/09/2006	18:52:10	18:52:11		yeah
163	05/09/2006	18:52:10	18:52:31				5 rows, 15 squares, 40 sticks									[1] Reference to whiteboard (whiteboardDoc)
	05/09/2006	18:52:32	18:52:38				[davidcyl has fully erased the chat message]
	05/09/2006	18:52:45	18:52:47				[davidcyl has fully erased the chat message]
164	05/09/2006	18:52:47	18:52:47				whoops
165	05/09/2006	18:52:49	18:53:07				and 6 rows, 21 squares, and 54 sticks
	05/09/2006		18:53:44	[137 moved some object/s ]
	05/09/2006		18:55:02	[137 moved some object/s ]
	05/09/2006		18:55:05	[137 moved some object/s ]
166	05/09/2006	18:54:48	18:55:06		alright people apparently LaTeX is like a 450 MB download... anyone have suggestions for a math equation editor?
	05/09/2006		18:55:09	[137 resized some objects ]
	05/09/2006		18:55:12	[137 moved some object/s ]
167	05/09/2006	18:55:18	18:55:20				i have mathtype here
168	05/09/2006	18:55:07	18:55:23		i know it's not necessary, but it would be nice to have a graphic demonstrating the summation notation for formulas :)
169	05/09/2006	18:55:28	18:55:32				there should be an online renderer
	05/09/2006	18:55:42	18:55:45	[137 has fully erased the chat message]
170	05/09/2006	18:55:34	18:55:46					or you could just text it with summ k=1 to inf
171	05/09/2006	18:55:51	18:55:53					or something like that
	05/09/2006	18:55:46	18:56:03	[137 has fully erased the chat message]
172	05/09/2006	18:56:04	18:56:15	Wait. Why are we using summations?
173	05/09/2006	18:56:30	18:56:36		for the formulas.. it looks nicer that way :)
174	05/09/2006	18:56:37	18:56:48		just downloaded trial of MathType, will install now...
175	05/09/2006	18:56:48	18:56:58									hope this doesnt sound too stupid, but wuts a summation
176	05/09/2006	18:57:13	18:57:14		installed :-)
	05/09/2006	18:57:06	18:57:22				[davidcyl has fully erased the chat message]
177	05/09/2006	18:57:12	18:57:34	The sum of all terms from a to b												[1] Reference to message No. 175 (Text: hope this doesnt sound too stupid, but wuts a summation )
178	05/09/2006	18:57:36	18:57:36		http://en.wikipedia.org/wiki/Sigma_notation
	05/09/2006	18:57:25	18:57:47				[davidcyl has fully erased the chat message]
179	05/09/2006	18:57:47	18:57:50				good idea
180	05/09/2006	18:58:04	18:58:11		don't worry nish, you'll learn all about it next year
181	05/09/2006	18:58:31	18:58:50					folks, you guys started late and so i think you should take the full hour you've got
182	05/09/2006	18:58:52	18:58:55					if you can
183	05/09/2006	18:58:58	18:58:58		alright
184	05/09/2006	18:58:58	18:59:07		i can be here as late as necessary (and reasonable)
185	05/09/2006	18:58:56	18:59:17					don't forget, we're gonna meet again same time, same place on Thursday!
186	05/09/2006	18:59:21	18:59:23				hows this http://www.forkosh.dreamhost.com/cgi-bin/mimetex.cgi?formdata=%5Csum_%7Bk%3D1%7D%5En+k
	05/09/2006	18:59:25	18:59:29	[137 has fully erased the chat message]
	05/09/2006	18:59:31	18:59:32	[137 has fully erased the chat message]
187	05/09/2006	18:59:32	18:59:37	So 4:00 or 4:30?												[1] Reference to message No. 178 (Text: http://en.wikipedia.org/wiki/Sigma_notation )
188	05/09/2006	18:59:57	19:00:01		i can't exactly copy URLs from here											[1] Reference to message No. 186 (Text: hows this http://www.forkosh.dreamhost.com/cgi-bin/mimetex.cgi?formdata=%5Csum_%7Bk%3D1%7D%5En+k )
189	05/09/2006	18:59:53	19:00:04	Misquoted.
190	05/09/2006	19:00:01	19:00:06		but is that a online renderer or your image
191	05/09/2006	19:00:00	19:00:08					what do you mean								[1] Reference to message No. 187 (Text: So 4:00 or 4:30? )
	05/09/2006	19:00:14	19:00:15	[137 has fully erased the chat message]
192	05/09/2006	19:00:16	19:00:22	Do we go on at 4 or 4:30?
193	05/09/2006	19:00:26	19:00:34	oh, shoot. 7 or 7:30?
194	05/09/2006	19:00:34	19:00:36		:30
195	05/09/2006	19:00:38	19:00:40		since we started around then
	05/09/2006	19:00:42	19:00:43		[Jason has fully erased the chat message]
196	05/09/2006	19:00:42	19:00:43	Right.
197	05/09/2006	19:00:43	19:00:44		anyways
198	05/09/2006	19:00:44	19:00:47		i got the thing in a GIF format
199	05/09/2006	19:00:44	19:00:47	Got it.
200	05/09/2006	19:00:50	19:01:01		i'll upload it to my personal web space and then we can use that image on the wiki
201	05/09/2006	19:00:29	19:01:04					well, it's supposed to start at 7:00 pm EST								[1] Reference to message No. 193 (Text: oh, shoot. 7 or 7:30? )
	05/09/2006	19:01:11	19:01:12	[137 has fully erased the chat message]
	05/09/2006	19:01:22	19:01:23	[137 has fully erased the chat message]
	05/09/2006	19:01:24	19:01:32	[137 has fully erased the chat message]
202	05/09/2006	19:01:27	19:01:34					so be there!!! ;-)
203	05/09/2006	19:01:33	19:01:48	Why can't we simply type it up as a formula?												[1] Reference to message No. 200 (Text: i'll upload it to my personal web space and then we can use that image on the wiki )
	05/09/2006	19:01:54	19:01:54		[Jason has fully erased the chat message]
204	05/09/2006	19:01:55	19:02:02		it'll be easier to read this way
205	05/09/2006	19:02:03	19:02:04		and it's quick
206	05/09/2006	19:02:00	19:02:09				forget it
207	05/09/2006	19:02:10	19:02:13				can't post iamges
208	05/09/2006	19:02:06	19:02:13		i've got the first one in a GIF file already... lemme resize it
209	05/09/2006	19:02:13	19:02:17				or links to images
210	05/09/2006	19:02:38	19:02:44		really? azemel said that we could earlier
211	05/09/2006	19:03:04	19:03:05		anywyas
212	05/09/2006	19:03:06	19:03:14		is there anything else related to the problem that we still need to discuss
213	05/09/2006	19:03:17	19:03:18				oh wait
214	05/09/2006	19:03:20	19:03:28					you can copy and paste graphic files
	05/09/2006	19:03:39	19:03:41					[azemel has fully erased the chat message]
215	05/09/2006	19:03:55	19:03:55				got it
216	05/09/2006	19:03:53	19:03:58	I dont\'t believe so.												[1] Reference to message No. 212 (Text: is there anything else related to the problem that we still need to discuss )
217	05/09/2006	19:03:59	19:03:59				http://mathforum.org/wiki/VMTStudents/?PatternsOfTheSticks
218	05/09/2006	19:04:03	19:04:08				you can't copy and paste without a host
219	05/09/2006	19:04:15	19:04:15		oh
220	05/09/2006	19:04:16	19:04:18		ok i'll try it
221	05/09/2006	19:05:15	19:05:15		got it
222	05/09/2006	19:05:19	19:05:34		sorry for the semi-low quality guys... i've got ClearType font smoothing on my screen and i guess that affects the quality
223	05/09/2006	19:05:54	19:05:57				i've already posted it
224	05/09/2006	19:05:58	19:05:59				on the wiki
225	05/09/2006	19:05:55	19:06:02					i wouldn't let the graphic thing slow you down
226	05/09/2006	19:06:19	19:06:20				we're done
227	05/09/2006	19:06:24	19:06:24					k
228	05/09/2006	19:06:20	19:06:28	Erm... What do you mean?												[1] Reference to message No. 225 (Text: i wouldn't let the graphic thing slow you down )
229	05/09/2006	19:06:34	19:06:38					the summation sign thing								[1] Reference to message No. 228 (Text: Erm... What do you mean? )
230	05/09/2006	19:06:41	19:06:43					that's all
231	05/09/2006	19:06:43	19:06:44	Ah.
232	05/09/2006	19:06:50	19:06:56				are there other problems we're supposed to work on?
	05/09/2006	19:06:53	19:07:02					[azemel has fully erased the chat message]
	05/09/2006	19:07:32	19:07:36					[azemel has fully erased the chat message]
	05/09/2006	19:07:37	19:07:37					[azemel has fully erased the chat message]
233	05/09/2006	19:07:37	19:08:04					well, if you're done with the sticks problem as it stands, then this might be a time to stop. there will be another problem on Thursday
	05/09/2006		19:08:19	[137 resized some objects ]
	05/09/2006		19:08:23	[137 resized some objects ]
234	05/09/2006	19:08:15	19:08:24					remember, 7 pm, Thursday, same room
235	05/09/2006	19:08:32	19:08:32		ok											[1] Reference to message No. 233 (Text: well, if you're done with the sticks problem as it stands, then this might be a time to stop. there will be another problem on Thursday )
236	05/09/2006	19:08:35	19:08:35				ok
237	05/09/2006	19:08:30	19:08:35	Right.
238	05/09/2006	19:08:40	19:08:40				look
	05/09/2006	19:08:39	19:08:41		[Jason has fully erased the chat message]
239	05/09/2006	19:08:41	19:08:41				http://www.forkosh.dreamhost.com/cgi-bin/mimetex.cgi?formdata=%5Cleft%28%5Csum_%7Bk%3D1%7D%5En+k%5Cright%29%2Bn
240	05/09/2006	19:09:16	19:09:33	How do you visit that w/o typing it in?												[1] Reference to message No. 239 (Text: http://www.forkosh.dreamhost.com/cgi-bin/mimetex.cgi?formdata=%5Cleft%28%5Csum_%7Bk%3D1%7D%5En+k%5Cright%29%2Bn )
241	05/09/2006	19:09:15	19:09:41					I assume you posted your results to the wiki, right?
	05/09/2006	19:09:47	19:09:49	[137 has fully erased the chat message]
	05/09/2006	19:09:50	19:09:51	[137 has fully erased the chat message]
242	05/09/2006	19:09:46	19:09:53					I don't think you can								[1] Reference to message No. 240 (Text: How do you visit that w/o typing it in? )
243	05/09/2006	19:09:52	19:09:54	They did.
244	05/09/2006	19:09:55	19:09:58					bummer
245	05/09/2006	19:10:01	19:10:02					good!!!
246	05/09/2006	19:10:04	19:10:06				copy and paste									[1] Reference to message No. 244 (Text: bummer )
247	05/09/2006	19:10:03	19:10:08					then let's call it an evening
248	05/09/2006	19:10:17	19:10:17				yes									[1] Reference to message No. 241 (Text: I assume you posted your results to the wiki, right? )
249	05/09/2006	19:10:19	19:10:19				ok
250	05/09/2006	19:10:13	19:10:21					thanks for coming and i hope you guys win!!!!
	05/09/2006	19:10:22	19:10:25	[137 has fully erased the chat message]
	05/09/2006	19:10:25	19:10:27				[davidcyl has fully erased the chat message]
251	05/09/2006	19:10:26	19:10:28	Thanks!
	05/09/2006	19:10:29	19:10:30	[137 has fully erased the chat message]
252	05/09/2006	19:10:27	19:10:33				:-) thanks. bye!
253	05/09/2006	19:10:33	19:10:34		thanks!											[1] Reference to message No. 239 (Text: http://www.forkosh.dreamhost.com/cgi-bin/mimetex.cgi?formdata=%5Cleft%28%5Csum_%7Bk%3D1%7D%5En+k%5Cright%29%2Bn )
	05/09/2006	19:10:26	19:10:35					[azemel has fully erased the chat message]
	05/09/2006	19:10:37	19:10:37		[Jason has fully erased the chat message]
254	05/09/2006		19:10:44				leaves the room
255	05/09/2006	19:10:37	19:10:51		and guys, i just realized that the summation notation stuff i put up is the SUM, not the formula
256	05/09/2006	19:10:51	19:10:59		so i guess i'll post the correct image later
257	05/09/2006	19:11:00	19:11:05		anyways, goodbye all
	05/09/2006	19:11:05	19:11:08	[137 has fully erased the chat message]
	05/09/2006	19:11:08	19:11:10	[137 has fully erased the chat message]
258	05/09/2006	19:11:10	19:11:13	Bye.
259	05/09/2006		19:11:14	leaves the room
260	05/09/2006	19:11:20	19:11:24					bye bye!!!
261	05/09/2006		19:11:29		leaves the room
262	05/09/2006	19:12:07	19:12:10									i g2g also
263	05/09/2006	19:12:12	19:12:24									sorry bout holdin u guys up
264	05/09/2006	19:12:20	19:12:26					be sure to come back next week ssjnish
265	05/09/2006	19:12:31	19:12:31									ok
266	05/09/2006	19:12:33	19:12:34									wait
267	05/09/2006	19:12:29	19:12:34					you didn't hold anybody up!
268	05/09/2006	19:12:36	19:12:45									is there one on thursday
269	05/09/2006	19:12:48	19:12:50					yes there is
270	05/09/2006	19:12:51	19:12:54					at 7 pm
	05/09/2006	19:12:56	19:12:59					[azemel has fully erased the chat message]
271	05/09/2006	19:12:59	19:13:03					eastern time
272	05/09/2006	19:13:09	19:13:09									kk
273	05/09/2006	19:13:08	19:13:16					thanks for slowing them down and getting them to explain
274	05/09/2006	19:13:27	19:13:27									?
275	05/09/2006	19:13:30	19:13:46									was thqat supposed to be a compliment...?
276	05/09/2006		19:13:52									leaves the room
277	05/09/2006	19:13:44	19:13:53					i liked your questions ... yes!
278	05/09/2006		19:20:05					leaves the room
279	05/10/2006		10:51:36							joins the room
280	05/10/2006		12:13:20					joins the room
281	05/10/2006		12:51:51					leaves the room
282	05/10/2006		17:45:54							leaves the room
283	05/11/2006		12:48:37										joins the room
284	05/11/2006		15:52:41						joins the room
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286	05/11/2006		16:26:47						leaves the room
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	05/11/2006		16:54:18							START:TextEditing
	05/11/2006		16:54:38							END:TextEditing
	05/11/2006		16:54:38							[jsarmi created a textbox ]
	05/11/2006		16:54:44							[jsarmi resized some objects ]
	05/11/2006		16:54:52							[jsarmi changed layout ]
	05/11/2006		16:54:59							START:TextEditing
	05/11/2006		16:55:13							END:TextEditing
	05/11/2006		16:55:13							[jsarmi changed the text to: Dear 137, davidcyl, Jason, and ssjnish, It seemed to us that you had a very productive first session exploring the given pattern of sticks and squares. We were especially interested in the variety of strategies you used, such as constructing the next steps of the pattern on the whiteboard, separating the pattern in horizontal and vertical lines (other teams did that as well!) and deriving a formula for that sum. As far as working as a math team, you built on each other’s ideas and tried to work with them in interesting ways. We find it very important that ssjnish felt comfortable asking the team to explain in detail the reasoning for the work completed (e.g. ssjnish 5/9/06 6:47:51 PM EDT: but how did u get that formula?), and that as a team you provided that explanation. It looked useful to us when your group tested together the formula you found. One question that was left unexplored was whether a recursive function shows better how the number of sticks and square grow. Someone offered that as a possibility but you opted for using a summation notation. We notice when ideas or questions are stated in a group but not discussed. What do you think about that situation and how groups deal with it? For the next step we will encourage you to think more about the different approaches and the problems that you can discover on your own which you find interesting to pursue. The VMT team. (Feel free to delete this note once everyone has read it) ]
288	05/11/2006		16:55:31							leaves the room
289	05/11/2006		18:54:11						joins the room
290	05/11/2006		18:55:13						leaves the room
291	05/11/2006		19:01:22						joins the room
292	05/11/2006		19:04:28		joins the room
293	05/11/2006		19:04:39	joins the room
294	05/11/2006		19:05:08						leaves the room
295	05/11/2006		19:05:26						joins the room
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	05/11/2006		19:05:59	[137 created a line ]
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	05/11/2006		19:06:05	[137 created a line ]
296	05/11/2006	19:05:42	19:06:06						so hi ya'll, I guess you're reading the pink textbox
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297	05/11/2006		19:06:10												joins the room
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298	05/11/2006		19:06:36			joins the room
	05/11/2006		19:06:49	[137 moved some object/s ]
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	05/11/2006		19:06:53	[137 moved some object/s ]
	05/11/2006		19:06:55	[137 moved some object/s ]
	05/11/2006		19:06:56	[137 moved some object/s ]
	05/11/2006		19:06:58	[137 moved some object/s ]
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	05/11/2006		19:07:12	[137 resized some objects ]
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299	05/11/2006	19:06:58	19:07:32						So everyone want to say hi or something just to show us we're here, kind of virual roll call
300	05/11/2006	19:07:38	19:07:38	Here.
301	05/11/2006	19:07:45	19:07:45		hi
302	05/11/2006	19:07:47	19:07:48			hi
303	05/11/2006	19:07:46	19:07:52		ssjnish says that his client is still loading
	05/11/2006		19:07:54		[Jason moved some object/s ]
	05/11/2006	19:07:56	19:08:04	[137 has fully erased the chat message]
	05/11/2006	19:08:03	19:08:29						[Cynthia has fully erased the chat message]
	05/11/2006		19:08:40	[137 created a line ]
	05/11/2006		19:08:42	[137 created a line ]
	05/11/2006		19:08:46	[137 created a line ]
	05/11/2006		19:08:54	[137 resized some objects ]
	05/11/2006		19:08:56	[137 resized some objects ]
	05/11/2006	19:08:31	19:08:58						[Cynthia has fully erased the chat message]
	05/11/2006		19:09:01	[137 resized some objects ]
	05/11/2006		19:09:04	[137 resized some objects ]
	05/11/2006	19:09:27	19:09:28		[Jason has fully erased the chat message]
304	05/11/2006	19:09:28	19:09:46		i think i might have a connection problem... all i'm seeing in this chat area is a series of small yellow squares
305	05/11/2006	19:10:19	19:10:20		anybody there?
306	05/11/2006	19:10:24	19:10:25			hi
307	05/11/2006	19:10:30	19:10:32		alright, got that
308	05/11/2006	19:10:45	19:10:58						so are you referring to something in the feedback jason
309	05/11/2006	19:11:09	19:11:15		no, i'm talking about this chat area
310	05/11/2006	19:11:18	19:11:23		i got the previous message here
311	05/11/2006	19:11:24	19:11:30		however i think my internet connection may be unstable
312	05/11/2006	19:11:35	19:12:07						oh i see, I thought you were posing a different math problem of little yellow squares :-)
313	05/11/2006	19:12:24	19:12:39						so do you all see a pink textbox with the feedback?
314	05/11/2006	19:12:43	19:12:43		yes
315	05/11/2006		19:13:31												leaves the room
	05/11/2006		19:13:41			[qwertyuiop moved some object/s ]
316	05/11/2006	19:13:52	19:13:53	Yes.
	05/11/2006	19:13:58	19:14:14						[Cynthia has fully erased the chat message]
	05/11/2006	19:15:04	19:15:17	[137 has fully erased the chat message]
317	05/11/2006	19:15:19	19:15:29	Is nobody posting or am I lagging?
318	05/11/2006	19:15:35	19:15:42			nobody is posting
319	05/11/2006		19:15:43							joins the room
320	05/11/2006	19:15:41	19:15:44		i don't think anyone is posing
321	05/11/2006	19:15:45	19:15:46	Whew.
	05/11/2006	19:15:50	19:15:52	[137 has fully erased the chat message]
322	05/11/2006		19:16:03						leaves the room
	05/11/2006	19:15:53	19:16:12		[Jason has fully erased the chat message]
	05/11/2006		19:16:33	[137 moved some object/s ]
323	05/11/2006	19:16:15	19:16:34							So... did you guys see the instructions in the View Topic window, (Session II)?
324	05/11/2006	19:16:18	19:16:37		ssjnish is currently restarting his laptop and will attempt to reconnect in a few minutes.
	05/11/2006		19:16:39	[137 resized some objects ]
325	05/11/2006	19:16:40	19:16:40		yes											[1] Reference to message No. 323 (Text: So... did you guys see the instructions in the View Topic window, (Session II)? )
326	05/11/2006	19:16:43	19:16:44	Same here.
	05/11/2006	19:16:52	19:16:52		[Jason has fully erased the chat message]
327	05/11/2006	19:16:58	19:17:00			where?										[1] Reference to message No. 323 (Text: So... did you guys see the instructions in the View Topic window, (Session II)? )
328	05/11/2006	19:16:50	19:17:08							great... then you can start and then bring ssjnish up to speed when he gets here
	05/11/2006	19:17:13	19:17:13							[jsarmi has fully erased the chat message]
329	05/11/2006	19:17:17	19:17:25	Up above the whiteboard on the right.
330	05/11/2006	19:17:26	19:17:33	The "View Topic" button.
331	05/11/2006	19:16:56	19:17:39		Please note that ssjnish and I share the same ISP -- InsightBB -- which is currently doing some maintenance work; they have warned us that during these few weeks, our network connections may be less reliable											[1] Reference to message No. 324 (Text: ssjnish is currently restarting his laptop and will attempt to reconnect in a few minutes. )
332	05/11/2006	19:17:52	19:18:02			yes										[1] Reference to message No. 330 (Text: The "View Topic" button. )
333	05/11/2006	19:17:56	19:18:07		ok, so with this aside-- i guess we should discuss our feedback from the last session
334	05/11/2006	19:18:23	19:18:34							make sure you bring qwertyuiop up to speed						[1] Reference to message No. 333 (Text: ok, so with this aside-- i guess we should discuss our feedback from the last session )
	05/11/2006	19:18:24	19:18:35	[137 has fully erased the chat message]
335	05/11/2006	19:18:41	19:18:41		ok
	05/11/2006	19:18:44	19:18:51		[Jason has fully erased the chat message]
	05/11/2006	19:18:51	19:19:12		[Jason has fully erased the chat message]
	05/11/2006	19:19:12	19:19:16		[Jason has fully erased the chat message]
336	05/11/2006	19:19:17	19:19:35		for the problems last session, we came up with formulas to find the values for the columns											[1] Reference to message No. 332 (Text: yes )
337	05/11/2006	19:19:53	19:20:02			in the view topic thing?
338	05/11/2006	19:19:38	19:20:03		You can see them to the left of this text; our formula for the total number of sticks or squares for any number N is given
339	05/11/2006	19:20:09	19:20:09		yes											[1] Reference to message No. 337 (Text: in the view topic thing? )
340	05/11/2006	19:20:12	19:20:12			ok
341	05/11/2006	19:20:09	19:20:17		that was the problem we were given
	05/11/2006	19:20:17	19:20:22		[Jason has fully erased the chat message]
342	05/11/2006	19:20:22	19:20:39		remains of our discussion is on the whiteboard and online wiki
	05/11/2006	19:20:59	19:21:01	[137 has fully erased the chat message]
343	05/11/2006	19:21:14	19:21:25	I think David forgot today... Our teacher didn't remind us.
	05/11/2006	19:21:37	19:21:46		[Jason has fully erased the chat message]
	05/11/2006		19:21:51	[137 moved some object/s ]
344	05/11/2006	19:22:23	19:22:35							I see... hopefully he will join you next Tuesday						[1] Reference to message No. 343 (Text: I think David forgot today... Our teacher didn't remind us. )
345	05/11/2006	19:22:43	19:23:35			n=3 is 3+2+1 squares, n=4 is 4+3+2+1 squares... how did you get n(1+n)/2
346	05/11/2006	19:23:41	19:23:42		oh
347	05/11/2006	19:23:42	19:23:53		that's the formula for finding a series of consecutive numbers
348	05/11/2006	19:23:55	19:24:08		1+2+3+4+...n = ((n)(n+1))/2
	05/11/2006		19:24:13		[Jason created a image ]
	05/11/2006		19:24:23		[Jason created a image ]
	05/11/2006		19:24:25		[Jason moved some object/s ]
	05/11/2006		19:24:26		[Jason moved some object/s ]
	05/11/2006		19:24:28		[Jason moved some object/s ]
	05/11/2006		19:24:29		[Jason deleted some object/s ]
349	05/11/2006	19:24:37	19:24:45		is anyone else getting boxes like these in their chat window?											[1] Reference to whiteboard (ImageStuff-1147389866453-24184240)
350	05/11/2006	19:24:30	19:24:55			i don't suppose the chat box is supposed to be jumping around my screen?
351	05/11/2006	19:25:00	19:25:00	NO,
352	05/11/2006	19:24:53	19:25:03							yes... they are new and represent activity on the whitebaord						[1] Reference to message No. 349 (Text: is anyone else getting boxes like these in their chat window? )
	05/11/2006		19:25:07	[137 moved some object/s ]
353	05/11/2006		19:25:10						joins the room
	05/11/2006		19:25:10	[137 moved some object/s ]
354	05/11/2006	19:25:10	19:25:10		i see
	05/11/2006	19:25:11	19:25:17							[jsarmi has fully erased the chat message]
355	05/11/2006	19:25:16	19:25:18	Oops.
356	05/11/2006	19:25:18	19:25:19	No.
357	05/11/2006	19:25:21	19:25:27	Didn't want to connote yelling.
	05/11/2006	19:25:34	19:25:37		[Jason has fully erased the chat message]
	05/11/2006	19:25:26	19:25:44							[jsarmi has fully erased the chat message]
358	05/11/2006	19:25:47	19:25:49							lol :-)						[1] Reference to message No. 357 (Text: Didn't want to connote yelling. )
	05/11/2006		19:25:57		[Jason deleted some object/s ]
359	05/11/2006	19:25:59	19:26:00							carry on
	05/11/2006		19:26:01		[Jason deleted some object/s ]
360	05/11/2006	19:26:09	19:26:09		ok											[1] Reference to whiteboard (whiteboardDoc)
361	05/11/2006	19:26:10	19:26:11		anyways
362	05/11/2006	19:26:16	19:26:32		so apparently there's something with a recursive sequence that we should discuss
	05/11/2006	19:26:38	19:26:40	[137 has fully erased the chat message]
	05/11/2006	19:26:42	19:26:43	[137 has fully erased the chat message]
363	05/11/2006	19:26:43	19:26:55	What was a recursice sequence again?
364	05/11/2006	19:26:53	19:27:03			recursive sequence?										[1] Reference to message No. 362 (Text: so apparently there's something with a recursive sequence that we should discuss )
365	05/11/2006	19:26:41	19:27:18		i think that an explicit formula is better, but a recursive one would show how the number of squares/sticks increases as N increases
366	05/11/2006	19:27:26	19:27:35		it's something like this:											[1] Reference to message No. 364 (Text: recursive sequence? )
367	05/11/2006	19:27:37	19:27:45		a(n) = 5+ a(n-1)
368	05/11/2006	19:27:46	19:27:53		where the things in parentheses are supposed to be subscripts
369	05/11/2006	19:27:55	19:28:07		so a recursive formula relies on the value of a previous function
370	05/11/2006	19:28:04	19:28:09	Ah, I see.												[1] Reference to message No. 365 (Text: i think that an explicit formula is better, but a recursive one would show how the number of squares/sticks increases as N increases )
371	05/11/2006	19:28:10	19:28:19		thus, you must specify something first, like a(1) = 4
372	05/11/2006	19:28:24	19:28:29			i get it										[1] Reference to message No. 369 (Text: so a recursive formula relies on the value of a previous function )
373	05/11/2006	19:28:52	19:28:54		great :-)
374	05/11/2006	19:29:03	19:30:07			for the number of squares, would that be: a(n)=n2-1
375	05/11/2006	19:29:58	19:30:15	so a(1)=1, a(n)=n+a(n-1)...												[1] Reference to message No. 371 (Text: thus, you must specify something first, like a(1) = 4 )
376	05/11/2006	19:30:15	19:30:18	For squares...
	05/11/2006		19:30:35	[137 resized some objects ]
	05/11/2006		19:30:38	[137 moved some object/s ]
377	05/11/2006	19:30:31	19:30:39		it looks right... lets check for a few values of N											[1] Reference to message No. 376 (Text: For squares... )
378	05/11/2006	19:31:01	19:31:06		when N = 1, #squares = 1
	05/11/2006	19:31:06	19:31:07	[137 has fully erased the chat message]
	05/11/2006	19:31:08	19:31:10	[137 has fully erased the chat message]
379	05/11/2006	19:31:11	19:31:19	When N is 2, a is 3.
380	05/11/2006	19:31:19	19:31:22		yup, i think thats right
	05/11/2006	19:31:37	19:31:39			[qwertyuiop has fully erased the chat message]
381	05/11/2006		19:31:47
382	05/11/2006	19:31:51	19:31:52	Oops.												[1] Reference to message No. 381 (Text: )
383	05/11/2006	19:32:15	19:33:06	b(1)=4, b(n)=b(n-1)+4(n)-(n-1)-(n-1), b is the number ofr sticks...
384	05/11/2006	19:33:08	19:33:30	So b(n)=b(n-1)+2n+2?
385	05/11/2006	19:33:42	19:33:51		assuming only (n-1) is a subscript?
386	05/11/2006	19:34:23	19:34:32			what does the subscript mean?										[1] Reference to message No. 385 (Text: assuming only (n-1) is a subscript? )
	05/11/2006	19:34:47	19:34:48		[Jason has fully erased the chat message]
387	05/11/2006	19:34:48	19:34:57		read "b of n minus 1"
	05/11/2006	19:35:00	19:35:00		[Jason has fully erased the chat message]
388	05/11/2006	19:35:02	19:35:03	Yes.												[1] Reference to message No. 385 (Text: assuming only (n-1) is a subscript? )
	05/11/2006	19:35:01	19:35:04		[Jason has fully erased the chat message]
389	05/11/2006	19:35:10	19:35:10		ok
390	05/11/2006	19:35:12	19:35:13		did u check that
	05/11/2006	19:35:19	19:35:20		[Jason has fully erased the chat message]
391	05/11/2006	19:35:21	19:35:39		looks correct
392	05/11/2006	19:35:40	19:35:45		how did you get it?
393	05/11/2006	19:36:16	19:36:23	There are n-1 overlaps here...
394	05/11/2006	19:36:23	19:36:24	Wait.
	05/11/2006		19:36:29	[137 created a scribble ]
	05/11/2006		19:36:30	[137 created a scribble ]
	05/11/2006		19:36:32	[137 created a scribble ]
395	05/11/2006	19:36:34	19:36:36	Those.
396	05/11/2006	19:36:36	19:36:43	And n-1 here:
397	05/11/2006	19:36:40	19:36:45			those?
	05/11/2006		19:36:46	[137 created a scribble ]
	05/11/2006		19:36:48	[137 created a scribble ]
	05/11/2006		19:36:49	[137 created a scribble ]
	05/11/2006		19:36:50	[137 created a scribble ]
398	05/11/2006	19:36:53	19:36:57		what do you mean by :"overlaps"
	05/11/2006	19:36:54	19:37:03	[137 has fully erased the chat message]
399	05/11/2006	19:37:03	19:37:17	They're counted twise; they belong to two boxes.
	05/11/2006		19:37:44	[137 created a scribble ]
	05/11/2006		19:37:45	[137 created a scribble ]
	05/11/2006		19:37:45	[137 created a scribble ]
	05/11/2006		19:37:46	[137 created a scribble ]
	05/11/2006		19:37:47	[137 created a scribble ]
	05/11/2006	19:38:04	19:38:04		[Jason has fully erased the chat message]
400	05/11/2006	19:38:05	19:38:13		are you guys still talking about that formula?
401	05/11/2006	19:38:15	19:38:22		because i dont think the overlap in the diagrams matters
402	05/11/2006	19:38:20	19:38:23	Yeah...
403	05/11/2006	19:38:29	19:38:36		if you are only calculating the number of sticks
404	05/11/2006	19:37:52	19:39:02			might be easier if you think of each square corisponding to 2 sides-the right and bottom sides, and then add the upper left border
405	05/11/2006	19:39:20	19:39:50			so it's number of squares*2 +...
406	05/11/2006	19:40:00	19:40:04		i don't see how the borders overlap
407	05/11/2006	19:40:05	19:40:10		if it's just right and bottom
408	05/11/2006	19:40:18	19:40:18	?												[1] Reference to message No. 406 (Text: i don't see how the borders overlap )
409	05/11/2006	19:40:09	19:40:32			number of squares*2 + n*2										[1] Reference to message No. 405 (Text: so it's number of squares*2 +... )
410	05/11/2006	19:40:44	19:40:46			overlap?										[1] Reference to message No. 406 (Text: i don't see how the borders overlap )
411	05/11/2006	19:41:12	19:41:23	Yeah, that should be right...												[1] Reference to message No. 409 (Text: number of squares*2 + n*2 )
	05/11/2006		19:41:29	[137 created a scribble ]
412	05/11/2006	19:41:19	19:41:48		well this requires you to first calculate number of squares; i think the formulas for each of these should be seperate											[1] Reference to message No. 409 (Text: number of squares*2 + n*2 )
413	05/11/2006	19:41:52	19:41:58		i liked the original formula
	05/11/2006	19:41:59	19:42:01		[Jason has fully erased the chat message]
	05/11/2006	19:41:59	19:42:05			[qwertyuiop has fully erased the chat message]
414	05/11/2006	19:42:01	19:42:05		in my quick checking it worked
415	05/11/2006	19:42:04	19:42:06	So did I...												[1] Reference to message No. 413 (Text: i liked the original formula )
416	05/11/2006	19:42:13	19:42:18	The first one seeemed simpler.
417	05/11/2006	19:42:31	19:42:39		but this one has a nice explanation :-)
418	05/11/2006	19:42:43	19:42:43		i mean											[1] Reference to message No. 409 (Text: number of squares*2 + n*2 )
419	05/11/2006	19:42:06	19:42:54			we already have the square formula; just include it: n(1+n)+n2
420	05/11/2006	19:43:15	19:43:16		yup
421	05/11/2006	19:43:14	19:43:41			that looks like the same thing as n*(N+3) at a glance...										[1] Reference to message No. 419 (Text: we already have the square formula; just include it: n(1+n)+n2 )
422	05/11/2006	19:43:18	19:43:51		so speaking of formulas, we got both explicit and recursive definitions for sticks/squares; explicit is easier while recursive shows how each step grows from the previous
423	05/11/2006	19:45:23	19:45:40			how do i type on the white board?
424	05/11/2006	19:45:46	19:45:55		click the text box (icon with A and lines in it)
	05/11/2006	19:45:59	19:45:59		[Jason has fully erased the chat message]
425	05/11/2006	19:45:46	19:46:01	Use the text box option, next to the camera.												[1] Reference to message No. 423 (Text: how do i type on the white board? )
	05/11/2006	19:46:00	19:46:03		[Jason has fully erased the chat message]
	05/11/2006	19:46:06	19:46:08	[137 has fully erased the chat message]
426	05/11/2006	19:46:11	19:46:13	Oops, two over.												[1] Reference to message No. 425 (Text: Use the text box option, next to the camera. )
427	05/11/2006	19:46:11	19:46:13		two away from camera											[1] Reference to message No. 425 (Text: Use the text box option, next to the camera. )
	05/11/2006	19:46:15	19:46:17		[Jason has fully erased the chat message]
428	05/11/2006	19:46:21	19:46:23			see it
	05/11/2006		19:46:28			START:TextEditing
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	05/11/2006		19:46:40			START:TextEditing
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	05/11/2006		19:46:45			START:TextEditing
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	05/11/2006		19:47:23			[qwertyuiop changed the text to: Formula for total # of squares: n(1+n)/2 a(n)=n+a(n-1) ]
429	05/11/2006	19:48:02	19:48:12	Er... Am I lagging or is nobody typing?
	05/11/2006	19:48:17	19:48:18		[Jason has fully erased the chat message]
430	05/11/2006	19:48:16	19:48:21			nobody is typing
431	05/11/2006	19:48:19	19:48:21		typing now :)
	05/11/2006	19:48:24	19:48:25			[qwertyuiop has fully erased the chat message]
432	05/11/2006	19:48:26	19:48:37			are there other problems to do?
433	05/11/2006	19:48:46	19:48:51	I do not think so...
434	05/11/2006	19:48:57	19:48:58		well
	05/11/2006	19:49:01	19:49:03							[jsarmi has fully erased the chat message]
435	05/11/2006	19:48:58	19:49:03		we are supposed to come up with some
436	05/11/2006	19:49:08	19:49:10			ok...
437	05/11/2006	19:48:57	19:49:13						did you view the topic for tonight, session 2
438	05/11/2006	19:49:16	19:49:17		WHAT IF? Mathematicians do not just solve other people's problems - they also explore little worlds of patterns that they define and find interesting. Think about other mathematical problems related to the problem with the sticks. For instance, consider other arrangements of squares in addition to the triangle arrangement (diamond, cross, etc.). What if instead of squares you use other polygons like triangles, hexagons, etc.? Which polygons work well for building patterns like this? How about 3-D figures, like cubes with edges, sides and cubes? What are the different methods (induction, series, recursion, graphing, tables, etc.) you can use to analye these different patterns?
	05/11/2006	19:49:04	19:49:30	[137 has fully erased the chat message]
439	05/11/2006	19:49:37	19:49:45						thanks, jason
	05/11/2006	19:49:54	19:49:55			[qwertyuiop has fully erased the chat message]
440	05/11/2006	19:49:44	19:50:07	Let's try diamonds first..												[1] Reference to message No. 438 (Text: WHAT IF? Mathematicians do not just solve other people's problems - they also explore little worlds of patterns that they define and find interesting. Think about other mathematical problems related to the problem with the sticks. For instance, consider other arrangements of squares in addition to the triangle arrangement (diamond, cross, etc.). What if instead of squares you use other polygons like triangles, hexagons, etc.? Which polygons work well for building patterns like this? How about 3-D figures, like cubes with edges, sides and cubes? What are the different methods (induction, series, recursion, graphing, tables, etc.) you can use to analye these different patterns? )
	05/11/2006		19:50:13	[137 created a scribble ]
441	05/11/2006	19:50:16	19:50:17		ok
	05/11/2006		19:50:19	[137 moved some object/s ]
	05/11/2006		19:50:22	[137 moved some object/s ]
442	05/11/2006	19:50:18	19:50:27		if the squares were arranged in a diamond-like shape...
	05/11/2006		19:50:27	[137 moved some object/s ]
	05/11/2006		19:50:31	[137 moved some object/s ]
	05/11/2006		19:50:35	[137 moved some object/s ]
	05/11/2006		19:50:37			[qwertyuiop created a line ]
443	05/11/2006	19:50:29	19:50:37		wait -- lemme make sure i read the directions carefully
	05/11/2006		19:50:39	[137 moved some object/s ]
	05/11/2006		19:50:39			[qwertyuiop created a line ]
	05/11/2006		19:50:40			[qwertyuiop created a line ]
	05/11/2006		19:50:40	[137 moved some object/s ]
	05/11/2006		19:50:42			[qwertyuiop created a line ]
	05/11/2006		19:50:43	[137 moved some object/s ]
444	05/11/2006	19:50:44	19:50:44		ok
	05/11/2006		19:50:45			[qwertyuiop created a line ]
	05/11/2006		19:50:46	[137 moved some object/s ]
	05/11/2006		19:50:46			[qwertyuiop created a line ]
	05/11/2006		19:50:48			[qwertyuiop created a line ]
	05/11/2006		19:50:48	[137 moved some object/s ]
	05/11/2006		19:50:49			[qwertyuiop created a line ]
	05/11/2006		19:50:51			[qwertyuiop created a line ]
	05/11/2006		19:50:51	[137 moved some object/s ]
	05/11/2006		19:50:52			[qwertyuiop created a line ]
	05/11/2006		19:50:54			[qwertyuiop created a line ]
	05/11/2006		19:50:54	[137 created a rectangle ]
	05/11/2006		19:50:56			[qwertyuiop created a line ]
	05/11/2006		19:50:57			[qwertyuiop created a line ]
	05/11/2006		19:50:57	[137 created a rectangle ]
	05/11/2006		19:50:58			[qwertyuiop created a line ]
445	05/11/2006	19:50:53	19:50:59		thanks for drawing :)
	05/11/2006		19:51:00			[qwertyuiop created a line ]
	05/11/2006		19:51:00	[137 changed layout ]
	05/11/2006		19:51:01	[137 created a rectangle ]
	05/11/2006		19:51:01			[qwertyuiop created a line ]
	05/11/2006		19:51:01	[137 created a rectangle ]
	05/11/2006		19:51:02	[137 created a rectangle ]
	05/11/2006		19:51:03	[137 created a rectangle ]
	05/11/2006		19:51:03			[qwertyuiop created a line ]
	05/11/2006		19:51:04			[qwertyuiop created a line ]
	05/11/2006		19:51:05			[qwertyuiop created a line ]
	05/11/2006		19:51:07	[137 created a rectangle ]
	05/11/2006		19:51:07			[qwertyuiop created a line ]
	05/11/2006		19:51:08	[137 created a rectangle ]
	05/11/2006		19:51:09			[qwertyuiop created a line ]
	05/11/2006		19:51:10			[qwertyuiop created a line ]
	05/11/2006		19:51:11			[qwertyuiop created a line ]
	05/11/2006		19:51:12	[137 moved some object/s ]
	05/11/2006		19:51:14			[qwertyuiop created a line ]
	05/11/2006		19:51:15			[qwertyuiop created a line ]
	05/11/2006		19:51:16			[qwertyuiop created a line ]
	05/11/2006		19:51:18			[qwertyuiop created a line ]
	05/11/2006		19:51:19	[137 created a rectangle ]
	05/11/2006		19:51:20			[qwertyuiop created a line ]
	05/11/2006		19:51:21			[qwertyuiop created a line ]
	05/11/2006		19:51:23	[137 created a rectangle ]
	05/11/2006		19:51:23			[qwertyuiop created a line ]
	05/11/2006		19:51:25			[qwertyuiop created a line ]
	05/11/2006		19:51:27			[qwertyuiop created a line ]
	05/11/2006		19:51:27	[137 created a rectangle ]
	05/11/2006		19:51:29			[qwertyuiop created a line ]
	05/11/2006		19:51:29	[137 created a rectangle ]
	05/11/2006		19:51:30			[qwertyuiop created a line ]
	05/11/2006		19:51:31	[137 created a rectangle ]
	05/11/2006		19:51:31			[qwertyuiop created a line ]
	05/11/2006		19:51:32			[qwertyuiop created a line ]
	05/11/2006		19:51:33	[137 created a rectangle ]
	05/11/2006		19:51:34			[qwertyuiop created a line ]
	05/11/2006		19:51:35	[137 created a rectangle ]
	05/11/2006	19:51:39	19:51:40	[137 has fully erased the chat message]
	05/11/2006	19:51:45	19:51:46			[qwertyuiop has fully erased the chat message]
	05/11/2006	19:51:45	19:51:47	[137 has fully erased the chat message]
446	05/11/2006	19:51:46	19:51:53			like that? (at the top)
447	05/11/2006	19:51:49	19:51:55	There's a square for later.
	05/11/2006		19:52:00	[137 created a rectangle ]
	05/11/2006		19:52:01	[137 created a rectangle ]
	05/11/2006		19:52:01	[137 created a rectangle ]
	05/11/2006		19:52:02	[137 created a rectangle ]
	05/11/2006		19:52:10	[137 created a rectangle ]
	05/11/2006		19:52:13	[137 moved some object/s ]
	05/11/2006		19:52:14	[137 moved some object/s ]
	05/11/2006		19:52:19	[137 moved some object/s ]
	05/11/2006		19:52:21	[137 moved some object/s ]
	05/11/2006		19:52:22	[137 moved some object/s ]
	05/11/2006		19:52:24	[137 moved some object/s ]
	05/11/2006		19:52:25	[137 moved some object/s ]
	05/11/2006		19:52:27	[137 moved some object/s ]
	05/11/2006		19:52:28	[137 moved some object/s ]
	05/11/2006		19:52:30	[137 moved some object/s ]
448	05/11/2006	19:53:52	19:53:52		ok
449	05/11/2006	19:53:54	19:53:57		sorry for the delay on my part
	05/11/2006	19:53:59	19:54:02		[Jason has fully erased the chat message]
450	05/11/2006	19:53:13	19:54:03	So the number of squares is n^2 +4, where n is a side length
451	05/11/2006	19:53:45	19:54:12			the "each square with 2 sides" thing doesn't work as neatly here
452	05/11/2006	19:54:03	19:54:13		if we look at rows, its 1, 3, 5, 3, 1
453	05/11/2006	19:54:22	19:54:28			how did you get that?										[1] Reference to message No. 450 (Text: So the number of squares is n^2 +4, where n is a side length )
454	05/11/2006	19:54:26	19:54:29		by side length you mean...											[1] Reference to message No. 450 (Text: So the number of squares is n^2 +4, where n is a side length )
	05/11/2006	19:54:34	19:54:35	[137 has fully erased the chat message]
	05/11/2006		19:54:42	[137 created a rectangle ]
	05/11/2006		19:54:44	[137 created a rectangle ]
	05/11/2006		19:54:46	[137 created a rectangle ]
455	05/11/2006	19:54:47	19:54:50	The orange.
	05/11/2006		19:54:55	[137 moved some object/s ]
	05/11/2006	19:54:58	19:55:00			[qwertyuiop has fully erased the chat message]
	05/11/2006		19:55:00	[137 moved some object/s ]
456	05/11/2006	19:54:58	19:55:01		ooohh... clever :-)
	05/11/2006		19:55:04	[137 moved some object/s ]
457	05/11/2006	19:55:00	19:55:08			is the saide lenght?										[1] Reference to message No. 455 (Text: The orange. )
	05/11/2006		19:55:14	[137 moved some object/s ]
	05/11/2006		19:55:16	[137 moved some object/s ]
	05/11/2006		19:55:18	[137 moved some object/s ]
458	05/11/2006	19:55:26	19:55:28	Yes.
	05/11/2006		19:55:30	[137 moved some object/s ]
	05/11/2006		19:55:31	[137 moved some object/s ]
	05/11/2006		19:55:37	[137 moved some object/s ]
	05/11/2006		19:55:38	[137 moved some object/s ]
	05/11/2006		19:55:39	[137 moved some object/s ]
	05/11/2006		19:55:43	[137 moved some object/s ]
	05/11/2006		19:55:45	[137 moved some object/s ]
459	05/11/2006	19:55:45	19:55:52		can you explain how you got that formula?
	05/11/2006		19:55:56	[137 moved some object/s ]
460	05/11/2006	19:55:39	19:55:57			so +4 is just for a side lenght of 3
461	05/11/2006	19:55:59	19:55:59			?
	05/11/2006		19:56:03	[137 moved some object/s ]
	05/11/2006		19:56:10	[137 moved some object/s ]
	05/11/2006		19:56:11	[137 moved some object/s ]
	05/11/2006		19:56:14	[137 moved some object/s ]
	05/11/2006		19:56:16	[137 moved some object/s ]
	05/11/2006		19:56:30	[137 created a rectangle ]
	05/11/2006		19:56:32		[Jason moved some object/s ]
	05/11/2006		19:56:33	[137 created a rectangle ]
462	05/11/2006	19:56:39	19:56:40	Erm...
463	05/11/2006	19:56:42	19:56:45	I'll make a new one.
464	05/11/2006	19:56:37	19:56:45		oops... sry i was trying to move that to the center
	05/11/2006		19:56:53	[137 created a rectangle ]
	05/11/2006		19:57:00	[137 moved some object/s ]
	05/11/2006		19:57:04	[137 changed layout ]
	05/11/2006		19:57:07	[137 created a rectangle ]
	05/11/2006		19:57:11	[137 created a rectangle ]
	05/11/2006		19:57:14	[137 created a rectangle ]
465	05/11/2006	19:57:16	19:57:17	There.
	05/11/2006		19:57:21	[137 changed layout ]
	05/11/2006		19:57:26	[137 created a rectangle ]
466	05/11/2006	19:57:25	19:57:28		thanks... and my apologies
467	05/11/2006	19:57:28	19:57:30	Erm...
	05/11/2006		19:57:33	[137 changed layout ]
	05/11/2006		19:57:34	[137 created a rectangle ]
	05/11/2006		19:57:35	[137 created a rectangle ]
	05/11/2006		19:57:35	[137 created a rectangle ]
	05/11/2006	19:57:37	19:57:39	[137 has fully erased the chat message]
468	05/11/2006	19:57:46	19:58:01	Why can't my fill thing un-fill stuff?
	05/11/2006		19:58:04	[137 created a rectangle ]
	05/11/2006		19:58:04	[137 created a rectangle ]
	05/11/2006		19:58:10	[137 created a rectangle ]
	05/11/2006		19:58:12	[137 created a rectangle ]
	05/11/2006		19:58:13	[137 created a rectangle ]
	05/11/2006		19:58:17	[137 created a rectangle ]
	05/11/2006		19:58:20	[137 created a rectangle ]
469	05/11/2006	19:58:18	19:58:23		just go up there and select "no fill"
	05/11/2006		19:58:24	[137 changed layout ]
	05/11/2006		19:58:31	[137 changed layout ]
470	05/11/2006	19:58:29	19:58:36		if that's the case, then i guess we have to use recursion again											[1] Reference to message No. 460 (Text: so +4 is just for a side lenght of 3 )
	05/11/2006		19:58:39	[137 changed layout ]
	05/11/2006	19:58:49	19:58:50	[137 has fully erased the chat message]
471	05/11/2006	19:58:54	20:00:17	It doesn't seem to work for clearing already painted areas.												[1] Reference to message No. 469 (Text: just go up there and select "no fill" )
472	05/11/2006	20:00:17	20:00:17	It doesn't seem to work for clearing already-painted areas.
	05/11/2006	20:00:17	20:00:18	[137 has fully erased the chat message]
	05/11/2006	20:00:18	20:00:18	[137 has fully erased the chat message]
	05/11/2006	20:00:18	20:00:18	[137 has fully erased the chat message]
473	05/11/2006	20:00:18	20:00:18	Can someone tell if my messages appeared on the chat? I can't see them/
	05/11/2006		20:00:18	START:TextEditing
	05/11/2006		20:00:22	END:TextEditing
474	05/11/2006	20:00:25	20:00:29	Oh, nevermind.
475	05/11/2006	20:00:30	20:00:30	Lag.
	05/11/2006		20:00:37	[137 created a rectangle ]
476	05/11/2006	20:00:26	20:00:39							tehy seem to be ok on my side 137 maybe a little bottleneck						[1] Reference to message No. 473 (Text: Can someone tell if my messages appeared on the chat? I can't see them/ )
	05/11/2006		20:00:46	[137 created a rectangle ]
	05/11/2006		20:00:48	[137 created a rectangle ]
477	05/11/2006	20:00:48	20:00:52		anyways, is that true?											[1] Reference to message No. 470 (Text: if that's the case, then i guess we have to use recursion again )
478	05/11/2006	19:59:31	20:00:57			i think NumberOfSides=NumberOfSquares*2+SideLength*3-2
	05/11/2006		20:01:05	[137 created a rectangle ]
	05/11/2006	20:01:11	20:01:16							[jsarmi has fully erased the chat message]
	05/11/2006		20:01:17	[137 resized some objects ]
479	05/11/2006	20:01:25	20:01:29		wait-- you gave a formula earlier
	05/11/2006		20:01:33	[137 changed layout ]
480	05/11/2006	20:01:30	20:01:34		lemme see if i can find it
	05/11/2006		20:01:38	[137 changed layout ]
481	05/11/2006	20:01:18	20:01:42			because it's like the first shape, but with 3 other edges										[1] Reference to message No. 478 (Text: i think NumberOfSides=NumberOfSquares*2+SideLength*3-2 )
	05/11/2006		20:01:54	[137 moved some object/s ]
482	05/11/2006	20:01:54	20:01:55		this one											[1] Reference to message No. 450 (Text: So the number of squares is n^2 +4, where n is a side length )
	05/11/2006		20:01:56	[137 moved some object/s ]
	05/11/2006		20:01:58	[137 moved some object/s ]
	05/11/2006		20:02:00	[137 moved some object/s ]
	05/11/2006		20:02:03	[137 moved some object/s ]
	05/11/2006		20:02:11	[137 moved some object/s ]
	05/11/2006		20:02:12	[137 moved some object/s ]
483	05/11/2006	20:02:04	20:02:12		oh but you're talking about # of sides
	05/11/2006		20:02:13	[137 moved some object/s ]
484	05/11/2006	20:02:18	20:02:19			yeah										[1] Reference to message No. 483 (Text: oh but you're talking about # of sides )
485	05/11/2006	20:02:35	20:02:44	Oh, yeah that's the blue in this diagram...
486	05/11/2006	20:02:45	20:02:45	Wait.
487	05/11/2006	20:02:34	20:02:50			the minus 2 is for the upper and left corners										[1] Reference to message No. 478 (Text: i think NumberOfSides=NumberOfSquares*2+SideLength*3-2 )
488	05/11/2006	20:02:55	20:03:00	Great. My controls froze.
489	05/11/2006	20:03:02	20:03:07	For the whiteboard.
490	05/11/2006	20:03:25	20:03:36							this happens if you go bak in the "history" of the whitebaord						[1] Reference to message No. 489 (Text: For the whiteboard. )
491	05/11/2006	20:03:37	20:03:58							Use the slider on the far left to come to the "present" moment of the whiteboard and your controls will get active again
	05/11/2006	20:03:59	20:04:00	[137 has fully erased the chat message]
492	05/11/2006	20:04:05	20:04:07	Thanks.												[1] Reference to message No. 491 (Text: Use the slider on the far left to come to the "present" moment of the whiteboard and your controls will get active again )
493	05/11/2006	20:04:11	20:04:13							sure
	05/11/2006		20:04:19	[137 created a rectangle ]
494	05/11/2006	20:04:21	20:04:42	So the blue is n^2 and there are 4 more squares outside for each...
	05/11/2006		20:04:43	[137 created a rectangle ]
	05/11/2006		20:04:48	[137 changed layout ]
	05/11/2006		20:04:50	[137 created a rectangle ]
	05/11/2006		20:04:53	[137 created a rectangle ]
	05/11/2006		20:04:57	[137 created a rectangle ]
	05/11/2006	20:04:59	20:05:00			[qwertyuiop has fully erased the chat message]
	05/11/2006		20:05:01	[137 created a rectangle ]
	05/11/2006		20:05:07	[137 moved some object/s ]
	05/11/2006		20:05:12	[137 created a rectangle ]
495	05/11/2006	20:05:01	20:05:12			that's number of squares?										[1] Reference to message No. 494 (Text: So the blue is n^2 and there are 4 more squares outside for each... )
496	05/11/2006	20:05:22	20:05:24	IT should be...
497	05/11/2006	20:05:25	20:05:26	shoot.
	05/11/2006		20:06:14	[137 moved some object/s ]
498	05/11/2006	20:06:15	20:06:23			or number of sides?										[1] Reference to message No. 495 (Text: that's number of squares? )
499	05/11/2006	20:06:31	20:06:37	I screwed up somewhere....
500	05/11/2006	20:06:43	20:06:50			what are you trying to find?										[1] Reference to message No. 499 (Text: I screwed up somewhere.... )
501	05/11/2006	20:07:14	20:07:19	The number of squares.
502	05/11/2006	20:07:26	20:07:36		actually... could this be figured out by using some geometric series
503	05/11/2006	20:07:39	20:08:18		the fact that, when the squares are arranged in a diamond shape result in 1+3+5+3+1 total squares in the diagram to the left, remind me of pascal's triangle											[1] Reference to whiteboard (whiteboardDoc)
504	05/11/2006	20:08:28	20:08:35		just a thought... not sure if it'll work
505	05/11/2006	20:07:34	20:08:35			using your previous method: SideLenght^2 + (SideLength-1)^2										[1] Reference to message No. 501 (Text: The number of squares. )
	05/11/2006	20:08:45	20:08:45			[qwertyuiop has fully erased the chat message]
506	05/11/2006	20:08:46	20:08:51			does that work?										[1] Reference to message No. 505 (Text: using your previous method: SideLenght^2 + (SideLength-1)^2 )
507	05/11/2006	20:09:09	20:10:06			the part in front of the plus is the large, rotatewd 45 square and the part after it is the smaller, not rotated squared										[1] Reference to message No. 505 (Text: using your previous method: SideLenght^2 + (SideLength-1)^2 )
508	05/11/2006	20:10:50	20:10:59			um... hello?
509	05/11/2006	20:11:02	20:11:03	Hi.
510	05/11/2006	20:11:11	20:11:17		well, looking at the center diagram with the orange boxed											[1] Reference to message No. 505 (Text: using your previous method: SideLenght^2 + (SideLength-1)^2 )
511	05/11/2006	20:11:14	20:11:18			but does that work?										[1] Reference to message No. 505 (Text: using your previous method: SideLenght^2 + (SideLength-1)^2 )
512	05/11/2006	20:11:19	20:11:20		boxes
513	05/11/2006	20:11:21	20:11:24		you'd be 1 off
514	05/11/2006	20:11:32	20:11:41		nvm, my arithmetic skills faltered ther
515	05/11/2006	20:11:42	20:11:42		e
	05/11/2006		20:11:47		[Jason created a rectangle ]
	05/11/2006		20:11:48		[Jason created a rectangle ]
516	05/11/2006	20:11:59	20:11:59		there
517	05/11/2006	20:11:53	20:12:03			checking for SideLenght=3...
	05/11/2006	20:12:27	20:12:28			[qwertyuiop has fully erased the chat message]
	05/11/2006	20:12:00	20:12:31		[Jason has fully erased the chat message]
518	05/11/2006	20:12:34	20:12:35		works											[1] Reference to message No. 517 (Text: checking for SideLenght=3... )
519	05/11/2006	20:12:29	20:12:36			yes, it works										[1] Reference to message No. 517 (Text: checking for SideLenght=3... )
520	05/11/2006	20:12:45	20:12:52		cool, so should we call this a formula
	05/11/2006	20:12:42	20:12:52	[137 has fully erased the chat message]
521	05/11/2006	20:12:52	20:12:57	I don't get why though...												[1] Reference to message No. 519 (Text: yes, it works )
	05/11/2006	20:13:13	20:13:28		[Jason has fully erased the chat message]
522	05/11/2006	20:13:28	20:13:29		i dont either											[1] Reference to message No. 521 (Text: I don't get why though... )
	05/11/2006		20:13:41	[137 created a rectangle ]
	05/11/2006		20:13:44	[137 created a rectangle ]
	05/11/2006		20:13:53	[137 created a rectangle ]
	05/11/2006		20:13:56	[137 created a rectangle ]
523	05/11/2006	20:13:02	20:14:10			I used your previous method: take the (orange) side; that^2 gives part of the shape...										[1] Reference to message No. 521 (Text: I don't get why though... )
	05/11/2006	20:14:01	20:14:18	[137 has fully erased the chat message]
524	05/11/2006	20:14:12	20:15:03			the rest happens to be a square with a side length of one less, therfore th "(SideLength-1)^2"										[1] Reference to message No. 523 (Text: I used your previous method: take the (orange) side; that^2 gives part of the shape... )
525	05/11/2006	20:15:06	20:15:10			does that make sense?
526	05/11/2006	20:15:41	20:15:42		i get it!
527	05/11/2006	20:15:42	20:15:43		clever :)
528	05/11/2006	20:15:46	20:15:48			137?
529	05/11/2006	20:15:50	20:15:56	Now I do.
530	05/11/2006	20:16:17	20:16:17		ok
	05/11/2006	20:16:21	20:16:26	[137 has fully erased the chat message]
531	05/11/2006	20:16:18	20:16:49		so in the little time we have left, should we discuss the second part of this problem -- what if instead of squares you used other polygons
532	05/11/2006	20:16:59	20:17:10			random thought: hypercubes
533	05/11/2006	20:16:56	20:17:19		not sure if i get that question, looks to me like the # of polygons will stay the same, only the # of sticks will vary based on the polygon
534	05/11/2006	20:17:20	20:17:22	Hm...
535	05/11/2006	20:17:23	20:17:32	Can't figure out what that should look like.
536	05/11/2006	20:17:29	20:17:33			which question?										[1] Reference to message No. 533 (Text: not sure if i get that question, looks to me like the # of polygons will stay the same, only the # of sticks will vary based on the polygon )
537	05/11/2006	20:17:34	20:17:44	Does anyone mind If I clear the board?
538	05/11/2006	20:17:58	20:17:59			no										[1] Reference to message No. 537 (Text: Does anyone mind If I clear the board? )
	05/11/2006		20:18:10	[137 moved some object/s ]
539	05/11/2006	20:18:11	20:18:12		go ahead
	05/11/2006		20:18:12	[137 moved some object/s ]
	05/11/2006		20:18:14	[137 moved some object/s ]
	05/11/2006		20:18:15	[137 moved some object/s ]
	05/11/2006		20:18:17	[137 moved some object/s ]
	05/11/2006		20:18:18	[137 moved some object/s ]
	05/11/2006		20:18:20	[137 resized some objects ]
	05/11/2006		20:18:22	[137 moved some object/s ]
540	05/11/2006	20:18:19	20:18:31			can i paste pictures onto the board?
	05/11/2006		20:18:34	[137 moved some object/s ]
	05/11/2006		20:18:41	[137 moved some object/s ]
	05/11/2006		20:18:42	[137 moved some object/s ]
	05/11/2006	20:18:42	20:18:43							[jsarmi has fully erased the chat message]
	05/11/2006		20:18:45	[137 moved some object/s ]
541	05/11/2006	20:18:44	20:18:46							yep						[1] Reference to message No. 540 (Text: can i paste pictures onto the board? )
542	05/11/2006	20:18:47	20:18:48	Yeah.
	05/11/2006		20:18:51	[137 moved some object/s ]
	05/11/2006		20:18:53	[137 resized some objects ]
	05/11/2006		20:18:55			[qwertyuiop created a image ]
543	05/11/2006	20:18:59	20:19:07			that's a hyper cube
544	05/11/2006	20:19:10	20:19:12		woah
545	05/11/2006	20:19:12	20:19:15		where'd that come from
546	05/11/2006	20:19:16	20:19:18	Wow.
547	05/11/2006	20:19:16	20:19:25			4 dimensional cube
548	05/11/2006	20:19:26	20:19:32			from wikipedia
	05/11/2006		20:19:45	[137 moved some object/s ]
	05/11/2006		20:19:46	[137 moved some object/s ]
	05/11/2006		20:19:48	[137 moved some object/s ]
	05/11/2006		20:19:51	[137 moved some object/s ]
	05/11/2006		20:19:52	[137 moved some object/s ]
	05/11/2006		20:19:54	[137 moved some object/s ]
	05/11/2006		20:19:56	[137 moved some object/s ]
	05/11/2006		20:19:57	[137 moved some object/s ]
	05/11/2006		20:19:59	[137 moved some object/s ]
	05/11/2006		20:20:01	[137 moved some object/s ]
549	05/11/2006	20:19:47	20:20:02		well maybe i'll understand this more if we dealt with 3-d cubes first
	05/11/2006		20:20:03	[137 moved some object/s ]
	05/11/2006	20:20:03	20:20:04		[Jason has fully erased the chat message]
550	05/11/2006	20:19:44	20:20:07			it can be seen as being made from 8 3D cubes
	05/11/2006		20:20:22	[137 created a rectangle ]
551	05/11/2006	20:20:22	20:20:22		ok
	05/11/2006		20:20:25	[137 created a rectangle ]
	05/11/2006		20:20:28	[137 created a rectangle ]
	05/11/2006		20:20:31	[137 created a rectangle ]
	05/11/2006		20:20:35	[137 created a rectangle ]
	05/11/2006		20:20:38	[137 moved some object/s ]
	05/11/2006		20:20:43	[137 created a line ]
	05/11/2006		20:20:45	[137 created a line ]
	05/11/2006		20:20:47	[137 created a line ]
	05/11/2006		20:20:49	[137 created a line ]
	05/11/2006		20:20:51	[137 created a line ]
	05/11/2006		20:20:54	[137 created a line ]
	05/11/2006		20:20:55	[137 created a line ]
	05/11/2006		20:20:57	[137 created a line ]
	05/11/2006		20:21:00	[137 created a line ]
	05/11/2006		20:21:02	[137 created a line ]
	05/11/2006		20:21:05	[137 created a line ]
	05/11/2006		20:21:07	[137 created a line ]
	05/11/2006		20:21:09	[137 created a line ]
	05/11/2006		20:21:10	[137 created a line ]
	05/11/2006		20:21:12	[137 created a line ]
	05/11/2006		20:21:15	[137 created a line ]
	05/11/2006	20:21:17	20:21:18	[137 has fully erased the chat message]
552	05/11/2006	20:21:19	20:21:19	?												[1] Reference to message No. 550 (Text: it can be seen as being made from 8 3D cubes )
	05/11/2006		20:21:24	[137 created a line ]
	05/11/2006		20:21:33	[137 resized some objects ]
553	05/11/2006	20:21:36	20:21:52			is that going to be a prism of the first problem?
	05/11/2006	20:22:06	20:22:10			[qwertyuiop has fully erased the chat message]
554	05/11/2006	20:22:12	20:22:40			to make it more 3D, you could continue the pattern along the new dimension
555	05/11/2006	20:22:46	20:22:57			not sure how you would draw that...
	05/11/2006	20:23:08	20:23:23		[Jason has fully erased the chat message]
556	05/11/2006	20:23:33	20:23:38		well going back to our session problems
557	05/11/2006	20:23:38	20:23:38		What are the different methods (induction, series, recursion, graphing, tables, etc.) you can use to analye these different patterns?
558	05/11/2006	20:23:45	20:23:57		i'd say series (recursive or explicit) for many of them
559	05/11/2006	20:24:46	20:24:49		anyone else?
560	05/11/2006	20:24:57	20:24:59			induction?
561	05/11/2006	20:25:57	20:25:58		what's that
562	05/11/2006	20:24:59	20:26:13						so i'm wondering if this is a good time to figure out the information that you are going to post to the wiki?
	05/11/2006	20:26:12	20:26:19			[qwertyuiop has fully erased the chat message]
563	05/11/2006	20:26:29	20:26:30		hmm
564	05/11/2006	20:26:24	20:26:30			the equations...
565	05/11/2006	20:26:30	20:26:55		well im not sure if we formulated too many questions to post, but i guess yeah we can write up our formulas and how we got them
566	05/11/2006	20:27:35	20:28:25			there are 4, I think: number of squares and number of sides for both diamonds and the first problem
567	05/11/2006	20:28:46	20:28:47		alright
	05/11/2006	20:28:48	20:28:48		[Jason has fully erased the chat message]
568	05/11/2006	20:28:49	20:29:05		last time we designated one person to write up the wiki... do you guys want to do that again or should we all assign each other some part to write
569	05/11/2006	20:29:27	20:29:35			we could just do it here
	05/11/2006	20:29:44	20:29:46		[Jason has fully erased the chat message]
570	05/11/2006	20:29:46	20:29:47		do what here
	05/11/2006	20:29:48	20:29:56			[qwertyuiop has fully erased the chat message]
571	05/11/2006	20:29:57	20:29:59			write it
572	05/11/2006	20:30:01	20:30:14			i can't get the typing thing to work in the board
573	05/11/2006	20:30:13	20:30:18		well it'll need to appear on the wiki someday
574	05/11/2006	20:30:26	20:30:35		yeah i guess we could write up the text here and someone can paste it into the wiki
575	05/11/2006	20:30:25	20:30:43			yes, we will put it on the wiki but write it here
576	05/11/2006	20:30:52	20:30:52		:-)
577	05/11/2006	20:30:50	20:30:59	You can't copy from here and then paste it there
578	05/11/2006	20:30:44	20:30:59							textboxes don't work for you qwerty?						[1] Reference to message No. 572 (Text: i can't get the typing thing to work in the board )
	05/11/2006		20:31:07							START:TextEditing
579	05/11/2006	20:31:15	20:31:17			no										[1] Reference to message No. 578 (Text: textboxes don't work for you qwerty? )
	05/11/2006		20:31:20							END:TextEditing
	05/11/2006		20:31:21							[jsarmi created a textbox ]
580	05/11/2006	20:31:29	20:31:33							try this one						[1] Reference to message No. 579 (Text: no )[2] Reference to whiteboard (whiteboardDoc)
	05/11/2006		20:31:43	START:TextEditing
	05/11/2006		20:31:44	END:TextEditing
	05/11/2006		20:31:51	START:TextEditing
581	05/11/2006	20:31:30	20:31:52			i can't select the text button at the top
	05/11/2006		20:32:00	END:TextEditing
	05/11/2006		20:32:00	[137 created a textbox ]
	05/11/2006		20:32:01	[137 moved some object/s ]
	05/11/2006		20:32:06	[137 moved some object/s ]
	05/11/2006		20:32:07	[137 moved some object/s ]
	05/11/2006		20:32:34		[Jason created a image ]
	05/11/2006		20:32:36		[Jason moved some object/s ]
	05/11/2006		20:32:37		[Jason moved some object/s ]
	05/11/2006		20:32:40		[Jason moved some object/s ]
582	05/11/2006	20:32:21	20:32:41							no luck? When you double click on it, it should let you type on it						[1] Reference to message No. 579 (Text: no )
	05/11/2006	20:32:45	20:32:46		[Jason has fully erased the chat message]
583	05/11/2006	20:32:46	20:32:48		this one right here?											[1] Reference to whiteboard (whiteboardDoc)
	05/11/2006		20:32:53			START:TextEditing
	05/11/2006		20:32:53			END:TextEditing
	05/11/2006		20:32:56			START:TextEditing
	05/11/2006		20:32:59			END:TextEditing
	05/11/2006		20:33:03		START:TextEditing
	05/11/2006		20:33:04			START:TextEditing
	05/11/2006		20:33:05			END:TextEditing
	05/11/2006		20:33:07			START:TextEditing
	05/11/2006		20:33:08			END:TextEditing
584	05/11/2006	20:32:56	20:33:12		click it once, make a square somewhere on the board, and then start tying
585	05/11/2006	20:33:12	20:33:13		typing*
586	05/11/2006	20:32:56	20:33:13							how about editing a texbox that is already there, like this one						[1] Reference to whiteboard ()
	05/11/2006		20:33:20		END:TextEditing
	05/11/2006		20:33:22		START:TextEditing
587	05/11/2006	20:33:21	20:33:31			now i can make one but not edit one...
588	05/11/2006	20:33:27	20:33:31		(double-click that one)
	05/11/2006		20:33:35			START:TextEditing
	05/11/2006		20:33:35			END:TextEditing
	05/11/2006		20:33:36			START:TextEditing
589	05/11/2006	20:33:26	20:33:37							this could be because you are back in the history of the whiteboard						[1] Reference to message No. 581 (Text: i can't select the text button at the top )
	05/11/2006		20:33:44			END:TextEditing
	05/11/2006		20:33:46			START:TextEditing
	05/11/2006		20:33:47			END:TextEditing
590	05/11/2006	20:33:46	20:33:48							strange						[1] Reference to message No. 587 (Text: now i can make one but not edit one... )
	05/11/2006		20:33:52		END:TextEditing
591	05/11/2006	20:33:50	20:33:59			yes, now it works. thanks
592	05/11/2006	20:34:03	20:34:04							great						[1] Reference to message No. 591 (Text: yes, now it works. thanks )
	05/11/2006	20:34:18	20:34:18		[Jason has fully erased the chat message]
593	05/11/2006	20:34:19	20:34:20		woohoo
	05/11/2006		20:34:25			START:TextEditing
	05/11/2006		20:34:28			END:TextEditing
594	05/11/2006	20:34:28	20:34:29							:-)
595	05/11/2006	20:34:25	20:34:30		should we all contribute something
	05/11/2006		20:34:31			START:TextEditing
596	05/11/2006	20:34:32	20:34:34		to the wiki
597	05/11/2006	20:34:39	20:34:56		like, should one person write about the formulas for the original problem and someone else write about the diamond one
598	05/11/2006	20:34:47	20:35:00	We will all contribute our ideas.
	05/11/2006		20:35:09			END:TextEditing
	05/11/2006		20:35:09			[qwertyuiop changed the text to: N(N+3) n(n-1)/2 ]
599	05/11/2006	20:35:22	20:35:22		ok
600	05/11/2006	20:35:15	20:35:37			those are the first 2...
	05/11/2006		20:35:42			START:TextEditing
601	05/11/2006	20:36:10	20:36:10		alright
	05/11/2006		20:36:17			END:TextEditing
	05/11/2006		20:36:17			[qwertyuiop changed the text to: sides: N(N+3) diamond: squares: n(n-1)/2 diamond: ]
602	05/11/2006	20:36:11	20:36:26		should i write about those? i'd like to if no one else wants to
603	05/11/2006	20:36:19	20:36:27			what were the diamond equations?
604	05/11/2006	20:36:37	20:36:38			sure										[1] Reference to message No. 602 (Text: should i write about those? i'd like to if no one else wants to )
605	05/11/2006	20:36:42	20:36:43		great
606	05/11/2006	20:36:43	20:36:53		i'll start a new text box and we can post to the wiki after i finish
607	05/11/2006	20:36:53	20:37:06		i'll need to go soon btw... im kinda getting hungry :-)
608	05/11/2006	20:37:04	20:37:11	one was n^2(n-1)^2
	05/11/2006		20:37:12		START:TextEditing
609	05/11/2006	20:37:17	20:37:18	Oops.
610	05/11/2006	20:37:22	20:37:22			+
611	05/11/2006	20:37:20	20:37:30	n^2 + (n-1)^2
612	05/11/2006	20:37:23	20:37:31		it appears that what we wrote to the wiki last time got deleted
	05/11/2006	20:37:36	20:37:37	[137 has fully erased the chat message]
	05/11/2006		20:37:41			START:TextEditing
613	05/11/2006	20:37:39	20:37:42	No, wrong page
	05/11/2006		20:37:59			END:TextEditing
	05/11/2006		20:37:59			[qwertyuiop changed the text to: sides: N(N+3) diamond: squares: n(n-1)/2 diamond: n^2+(n-1)^2 ]
614	05/11/2006	20:37:59	20:38:00		o
615	05/11/2006	20:38:03	20:38:10		i guess we were the only ones posting last time
616	05/11/2006	20:38:10	20:38:18		so i guess the only thing we really need to post is the diamonds problem
617	05/11/2006	20:38:30	20:38:47			what was the equation for the number of squares in a diamond?
618	05/11/2006	20:38:52	20:38:54		lemme see if i can find it
	05/11/2006		20:38:55		END:TextEditing
	05/11/2006		20:38:55		[Jason created a textbox ]
	05/11/2006		20:38:56		[Jason deleted some object/s ]
	05/11/2006		20:38:58		[Jason deleted some object/s ]
619	05/11/2006	20:39:48	20:39:55		sidelength^2 + (sidelength-1)^2											[1] Reference to message No. 505 (Text: using your previous method: SideLenght^2 + (SideLength-1)^2 )
620	05/11/2006	20:39:55	20:39:55		i think
	05/11/2006		20:40:25			START:TextEditing
621	05/11/2006	20:40:35	20:40:37	Ya, it is.												[1] Reference to message No. 620 (Text: i think )
	05/11/2006		20:40:43			END:TextEditing
622	05/11/2006	20:40:43	20:40:43		great
	05/11/2006		20:40:49	[137 resized some objects ]
	05/11/2006	20:40:52	20:41:00			[qwertyuiop has fully erased the chat message]
623	05/11/2006	20:40:52	20:41:01		here, i'll start making a diagram for the problem for the wiki
624	05/11/2006	20:41:03	20:41:12			that's for squares?										[1] Reference to message No. 619 (Text: sidelength^2 + (sidelength-1)^2 )
	05/11/2006	20:41:05	20:41:15		[Jason has fully erased the chat message]
625	05/11/2006	20:41:16	20:41:17	Yes.
626	05/11/2006	20:41:19	20:41:22		for the diamonds i thought...
627	05/11/2006	20:41:23	20:41:35			oops. I ment sides. I'll look for it.										[1] Reference to message No. 617 (Text: what was the equation for the number of squares in a diamond? )
628	05/11/2006	20:41:31	20:41:38	FOr the number of squares in a diamond formation.												[1] Reference to message No. 626 (Text: for the diamonds i thought... )
629	05/11/2006	20:41:43	20:41:43		yeah											[1] Reference to message No. 628 (Text: FOr the number of squares in a diamond formation. )
630	05/11/2006	20:43:21	20:43:25			is this it?										[1] Reference to message No. 478 (Text: i think NumberOfSides=NumberOfSquares*2+SideLength*3-2 )
631	05/11/2006	20:43:41	20:43:41		yes
	05/11/2006		20:43:55			START:TextEditing
	05/11/2006	20:44:25	20:44:28	[137 has fully erased the chat message]
	05/11/2006		20:44:30			END:TextEditing
	05/11/2006		20:44:30			[qwertyuiop changed the text to: sides: N(N+3) diamond: (n^2+(n-1)^2)*2+n*3-2 squares: n(n-1)/2 diamond: n^2+(n-1)^2 ]
632	05/11/2006	20:44:33	20:44:51	Sorry, but I have to go now... Have a class soon.
633	05/11/2006	20:45:08	20:45:08		cya
634	05/11/2006	20:45:02	20:45:11							Next session is next Tuesday, same time 137
635	05/11/2006	20:45:13	20:45:15	Right.
636	05/11/2006		20:45:19	leaves the room
637	05/11/2006	20:45:23	20:45:34							Are you guys ok writing your notes on the Wiki?
638	05/11/2006	20:45:40	20:45:45			where's the wiki?
	05/11/2006	20:45:42	20:45:45		[Jason has fully erased the chat message]
639	05/11/2006	20:45:50	20:45:50		http://mathforum.org/wiki/VMTStudents/VMTStudents?OtherSticksProblemIdeas
640	05/11/2006	20:45:51	20:45:56		there's a link under "view topic"
641	05/11/2006	20:46:03	20:46:23							to copy this URL use th Alt key when highlighting the text and then do copy						[1] Reference to message No. 639 (Text: http://mathforum.org/wiki/VMTStudents/VMTStudents?OtherSticksProblemIdeas )
642	05/11/2006	20:46:23	20:46:27			going there..										[1] Reference to message No. 639 (Text: http://mathforum.org/wiki/VMTStudents/VMTStudents?OtherSticksProblemIdeas )
643	05/11/2006	20:47:04	20:47:18			can't seem to copy it. i'll just type it.										[1] Reference to message No. 642 (Text: going there.. )
644	05/11/2006	20:47:32	20:47:34		or just follow the link
645	05/11/2006	20:47:37	20:47:49		anyhow, i got a diagram of the diamonds thing at http://mathforum.org/wikis/uploads/diamonds.PNG
646	05/11/2006	20:48:36	20:49:18		qwertyuiop if you start the wiki writeup it would be appreciated... i have to go now but i can edit/contribute to our writeup later											[1] Reference to message No. 645 (Text: anyhow, i got a diagram of the diamonds thing at http://mathforum.org/wikis/uploads/diamonds.PNG )
647	05/11/2006	20:49:19	20:49:22		i'll stay logged into this thing
648	05/11/2006	20:49:25	20:49:29		goodbye for now..
649	05/11/2006	20:49:37	20:49:42							See you next week, Jason
	05/11/2006	20:50:01	20:50:01			[qwertyuiop has fully erased the chat message]
650	05/11/2006	20:50:04	20:50:06						bye jason
651	05/11/2006	20:50:01	20:50:11			who's putting it on the wiki?										[1] Reference to message No. 645 (Text: anyhow, i got a diagram of the diamonds thing at http://mathforum.org/wikis/uploads/diamonds.PNG )
	05/11/2006	20:50:34	20:50:38							[jsarmi has fully erased the chat message]
652	05/11/2006	20:50:41	20:51:13							You could write as much as you can now, and Jason will complete it later. Is that ok?						[1] Reference to message No. 651 (Text: who's putting it on the wiki? )
653	05/11/2006	20:51:19	20:51:20			ok
	05/11/2006		20:51:22			START:TextEditing
654	05/11/2006	20:51:27	20:51:29			bye
655	05/11/2006	20:51:26	20:51:38							Great...see you next week on Tuesday!
656	05/11/2006	20:51:40	20:51:51							Thanks for attending today!
	05/11/2006		20:51:56			END:TextEditing
657	05/11/2006		20:51:56			leaves the room
658	05/11/2006		20:52:01							leaves the room
659	05/11/2006	20:53:37	20:53:43						Bye everyone. Thanks
660	05/11/2006		20:53:46						leaves the room
661	05/11/2006		21:17:33		leaves the room
662	05/16/2006		16:08:08							joins the room
663	05/16/2006		17:20:42								joins the room
	05/16/2006		17:28:27								[nan moved some object/s ]
	05/16/2006		17:56:20							START:TextEditing
	05/16/2006		17:56:42							END:TextEditing
	05/16/2006		17:56:42							[jsarmi created a textbox ]
	05/16/2006		17:56:47							[jsarmi moved some object/s ]
	05/16/2006		17:56:51							[jsarmi resized some objects ]
	05/16/2006		17:56:54							[jsarmi moved some object/s ]
	05/16/2006		17:57:07							[jsarmi changed layout ]
664	05/16/2006		17:57:15							leaves the room
665	05/16/2006		19:01:25		joins the room
666	05/16/2006		19:02:22	joins the room
667	05/16/2006	19:02:30	19:02:37								hi Jason and 137, welcome back
668	05/16/2006	19:02:49	19:02:49		hi
669	05/16/2006	19:03:05	19:03:06	Hi.
670	05/16/2006	19:02:56	19:03:09								i'll be your facilitator tonight
671	05/16/2006	19:02:51	19:03:13		it looks like ssjnish is having connection problems again, even after i pointed him to an email on how to clear his Java cache
	05/16/2006		19:03:34	[137 moved some object/s ]
672	05/16/2006		19:03:45			joins the room
	05/16/2006		19:04:04	[137 moved some object/s ]
	05/16/2006		19:04:07	[137 moved some object/s ]
	05/16/2006		19:04:09	[137 moved some object/s ]
673	05/16/2006	19:04:07	19:04:13								hi qwertyuiop
	05/16/2006		19:04:14	[137 moved some object/s ]
	05/16/2006		19:04:17	[137 moved some object/s ]
674	05/16/2006	19:04:23	19:04:23			hi
675	05/16/2006	19:04:24	19:04:36								do any of you know if david is coming?
676	05/16/2006	19:04:33	19:04:41	So we do what we did last time again?
677	05/16/2006	19:04:46	19:04:47								yes					[1] Reference to message No. 676 (Text: So we do what we did last time again? )
678	05/16/2006	19:04:42	19:04:52	I forgot to ask David at school.												[1] Reference to message No. 675 (Text: do any of you know if david is coming? )
679	05/16/2006	19:04:59	19:05:04	I don't think he'd remember.
680	05/16/2006	19:04:48	19:05:11								first take a few minutes to read the feedback posted on the whiteboard
681	05/16/2006	19:05:19	19:05:21								no problem					[1] Reference to message No. 678 (Text: I forgot to ask David at school. )
682	05/16/2006	19:05:23	19:05:27								i guess we can start
	05/16/2006	19:05:29	19:05:38								[nan has fully erased the chat message]
683	05/16/2006	19:05:38	19:05:48								david can join later when he comes
684	05/16/2006	19:05:53	19:05:54	Right.
	05/16/2006	19:05:55	19:05:58	[137 has fully erased the chat message]
	05/16/2006		19:06:11	[137 moved some object/s ]
	05/16/2006		19:06:19	[137 resized some objects ]
	05/16/2006		19:06:34	[137 resized some objects ]
685	05/16/2006	19:06:19	19:06:34			has everyone read the green text box?
	05/16/2006		19:06:37	[137 resized some objects ]
	05/16/2006		19:06:39	[137 resized some objects ]
686	05/16/2006	19:06:43	19:06:44		one sec
687	05/16/2006	19:06:43	19:06:45	Yes...
	05/16/2006		19:06:50	[137 resized some objects ]
	05/16/2006		19:06:56	[137 resized some objects ]
688	05/16/2006	19:07:00	19:07:01		alright im done
689	05/16/2006	19:06:27	19:07:02								did you see some little squares aftermessage? i haven't seen thoese before, interesting
690	05/16/2006	19:07:10	19:07:11			yes
691	05/16/2006	19:07:07	19:07:12		yeah, they just indicate whiteboard activity
692	05/16/2006	19:07:31	19:07:32	Oh.
693	05/16/2006	19:07:22	19:07:40								i see. i was on a leave for two weeks and this version is the latest					[1] Reference to message No. 691 (Text: yeah, they just indicate whiteboard activity )
	05/16/2006		19:07:52	[137 resized some objects ]
	05/16/2006		19:07:56	[137 resized some objects ]
	05/16/2006		19:07:59	[137 resized some objects ]
	05/16/2006		19:08:06	[137 resized some objects ]
	05/16/2006		19:08:15	[137 moved some object/s ]
	05/16/2006		19:08:24	[137 moved some object/s ]
	05/16/2006		19:08:32	[137 moved some object/s ]
	05/16/2006		19:08:33