Dataset2/D2TCSS

From Jsarmi

Revision as of 19:19, 29 November 2007

Group Trajectory

 Session 1: 
 Session 2: Feedback attended to
 Session 3: 
 Session 4: 

Group composition: Stable

 Session 1:  js   dc   ot   ss(L)
 Session 2:           
 Session 3:  
 Session 4:
 
 (L) Late

Session I

They join within seconds:

 Jason joins the room 5/9/06 6:24:03 PM EDT
 davidcyl joins the room 5/9/06 6:24:04 PM EDT
 137 joins the room 5/9/06 6:24:15 PM EDT

We did this in class

Notice how it is 137 who ends up posting the formula

 Jason 5/9/06 6:25:44 PM EDT: ooh we just did this in math class about a week ago! :-)
 p M M M
 azemel 5/9/06 6:25:54 PM EDT: if you have any questions, just ask
 Jason 5/9/06 6:25:55 PM EDT: well, not the exact thing, but sequences and series
 p M M
 Jason 5/9/06 6:26:03 PM EDT: anyhow
 p M M M M M M M
 Jason 5/9/06 6:26:21 PM EDT: so do we see how the number of sticks grows in a sequence?
 davidcyl 5/9/06 6:26:25 PM EDT: ok i've drawn n=4,5,6
 Jason 5/9/06 6:26:29 PM EDT: 4(+6) = 10
 Jason 5/9/06 6:26:36 PM EDT: 10(+8) = 18
 p M M
 Jason 5/9/06 6:26:48 PM EDT: i'm guessing 18(+10) = 28 for the next one, according to this pattern
 davidcyl 5/9/06 6:27:32 PM EDT: the nth pattern has n more squares than the (n-1)th pattern
 davidcyl 5/9/06 6:27:55 PM EDT: basically it's 1+2+..+(n-1)+n for the number of squares in the nth pattern
 137 5/9/06 6:28:16 PM EDT: so n(n+1)/2
 davidcyl 5/9/06 6:28:24 PM EDT: and we can use the gaussian sum to determine the sum: n(1+n)/2
 davidcyl 5/9/06 6:28:36 PM EDT: 137 got it

Recursive or Explicit?

Notice that Jason ASKS and david offers his opinion. See Session II

 davidcyl 5/9/06 6:29:31 PM EDT: well to find the number of sticks:
 davidcyl 5/9/06 6:29:39 PM EDT: let's look on the board
 p M M M
 Jason 5/9/06 6:29:54 PM EDT: should we use a recursive or explicit definition for it
 p M M
 davidcyl 5/9/06 6:30:20 PM EDT: i don't think we need recursion

Horizontal and Vertical

As in Team B

(david circles horizontal lines in a pattern diagram on the whiteboard)
davidcyl 5/9/06 6:32:21 PM EDT: 137: i'm separating the sticks into vertical and horizontal sticks
 davidcyl 5/9/06 6:30:33 PM EDT: it's simpler to express it as 1+2+...+n

Not Shared

Disoriented, then MY formula

 davidcyl 5/9/06 6:32:30 PM EDT: wait what are you working on?
 Jason 5/9/06 6:32:32 PM EDT: wait lemme check
 davidcyl 5/9/06 6:32:35 PM EDT: (to 137)
 137 5/9/06 6:32:46 PM EDT: Great. Confused.
 Jason 5/9/06 6:33:03 PM EDT: 137 are you talking about # sticks or squares
 137 5/9/06 6:33:09 PM EDT: Sticks.
 Jason 5/9/06 6:33:18 PM EDT: ok
 davidcyl 5/9/06 6:33:21 PM EDT: i would think it's 2(n(1+n)/2) + n + n
 Jason 5/9/06 6:33:23 PM EDT: well i think my formula works
 Jason 5/9/06 6:33:33 PM EDT: provided that you have a value for N

but later (after an interruption)

 davidcyl 5/9/06 6:35:03 PM EDT: this simplifies to n(1+n) + 2n, or n(3+n)
 davidcyl 5/9/06 6:35:09 PM EDT: so jason, you're right
 Jason 5/9/06 6:35:16 PM EDT: :-)
 Jason 5/9/06 6:35:36 PM EDT: so now onto a formula for the total number of squares

Ssjnish joins

ssjnish joins the room 5/9/06 6:34:25 PM EDT

Didn't we do that?

 davidcyl 5/9/06 6:35:03 PM EDT: this simplifies to n(1+n) + 2n, or n(3+n)
 davidcyl 5/9/06 6:35:09 PM EDT: so jason, you're right
 Jason 5/9/06 6:35:16 PM EDT: :-)
 Jason 5/9/06 6:35:36 PM EDT: so now onto a formula for the total number of squares
 davidcyl 5/9/06 6:35:42 PM EDT: ok let's complete the table
 Jason 5/9/06 6:35:46 PM EDT: if you take the change in the change of the number of squares, it's constant
 137 5/9/06 6:36:10 PM EDT: Didn't we do that?
 (points to Jason's message on 6:35:36 PM)
 davidcyl 5/9/06 6:36:19 PM EDT: yes
 Jason 5/9/06 6:36:27 PM EDT: oh, sorry i guess i must've not caught that
 davidcyl 5/9/06 6:36:33 PM EDT: look up
 (points to davidcyl 5/9/06 6:28:24 PM EDT: and we can use the gaussian sum to determine the sum: n(1+n)/2)
 Jason 5/9/06 6:36:33 PM EDT: could someone post it in a text box on the whiteboard
 davidcyl 5/9/06 6:36:38 PM EDT: sure
 azemel 5/9/06 6:36:40 PM EDT: be sure that SSJNISH is up to speed folks
 (Textbox created) 

A summary for Ssjnish

Notice the diffeence between We've figured out and I divided

 davidcyl 5/9/06 6:38:30 PM EDT: basically, we've figured out that the number of squares in the nth pattern is 1 + 2 + ... + n
 p M
 137 5/9/06 6:38:33 PM EDT: It was blinding.
 p M M M M
 davidcyl 5/9/06 6:39:26 PM EDT: then, to find the number of sticks, I divided the figure into "vertical sticks" (|) and "horizontal   sticks" (--)
 Jason 5/9/06 6:39:41 PM EDT: the formulas are on the Whiteboard
 azemel 5/9/06 6:39:56 PM EDT: don't forget to post your ideas to the wiki when you think it's time!
 davidcyl 5/9/06 6:40:15 PM EDT: the number of vertical sticks is (1 + 2 + 3 + ... + n)+ n, and the number of horizontal sticks is the same
 p M

Ssjnish asks for an explanation

 ssjnish 5/9/06 6:45:11 PM EDT: 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..
 azemel 5/9/06 6:45:44 PM EDT: can you tell us what's puzzling you?
 Jason 5/9/06 6:46:07 PM EDT: 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
 ssjnish 5/9/06 6:46:12 PM EDT: the derivation of the number of squares