Dataset2/D2TCSS - Revision history

Jsarmi: /* Wouldn't this work? */

Jsarmi — Sun, 04 May 2008 19:51:58 GMT

Wouldn't this work?

←Older revision		Revision as of 19:51, 4 May 2008
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	Later QW makes a series of very interesting graphs that form a proposal for how to calculate the number of edges and posts:		Later QW makes a series of very interesting graphs that form a proposal for how to calculate the number of edges and posts:
		+
		+	qwertyuiop 5/18/06 7:48:21 PM EDT: an idea: Each cube is assigned to 3 edges. Then add the edges on the diagonalish face.
		+	qwertyuiop 5/18/06 7:48:44 PM EDT: does that make sense?
		+	137 5/18/06 7:48:58 PM EDT: Not really...
		+	qwertyuiop 5/18/06 7:49:13 PM EDT: let me think how to explain it...
		+	Jason 5/18/06 7:49:13 PM EDT: well some would be the same
		+	p M M M
		+	qwertyuiop 5/18/06 7:51:36 PM EDT: oops
		+	p M
		+	qwertyuiop 5/18/06 7:52:44 PM EDT: see those 3 highlighted edges?
		+	Jason 5/18/06 7:53:32 PM EDT: yeah
		+	Jason 5/18/06 7:53:37 PM EDT: theyre in red
		+	qwertyuiop 5/18/06 7:54:09 PM EDT: those would be the edges assigned to that cube (the cube at the bottom corner)
		+	qwertyuiop 5/18/06 7:54:15 PM EDT: still make sense?
		+

	qwertyuiop 5/18/06 8:02:49 PM EDT: so the first part of the equation would be 3 times the number of cubes		qwertyuiop 5/18/06 8:02:49 PM EDT: so the first part of the equation would be 3 times the number of cubes

Jsarmi: /* Wouldn't this work? */

Jsarmi — Sun, 04 May 2008 19:46:16 GMT

Wouldn't this work?

←Older revision		Revision as of 19:46, 4 May 2008
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	===Wouldn't this work?===		===Wouldn't this work?===
-	OT points to his earlier posting indicating a reuse of something they did in last session on the hexagon:	+	OT points to his earlier posting indicating a reuse of something they did in last session on the hexagon.
		+	Notice that "overlap" resurfaces as a relevant concern.

	137 5/18/06 7:41:52 PM EDT: Wouldn't this work? [Points to: I think we should just look at it in 3 groups of parallel lines like last time.]		137 5/18/06 7:41:52 PM EDT: Wouldn't this work? [Points to: I think we should just look at it in 3 groups of parallel lines like last time.]

Jsarmi: /* Like we said earlier */

Jsarmi — Sun, 04 May 2008 19:43:54 GMT

Like we said earlier

←Older revision		Revision as of 19:43, 4 May 2008
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	137 5/18/06 7:29:34 PM EDT: 10+6+3+1=20.		137 5/18/06 7:29:34 PM EDT: 10+6+3+1=20.

		+
		+	===The evolution of Whiteboard Notes===
		+	It is interesting that this team keeps all its results in a single textbox on the whiteboard. In the wiki, there is more explanation but on the whiteboard it is a place to keep all the formulas organized and, as new formulas/results are added, some of the existing labels are changes to represent the "expanding" notions that they are working with. For example, in the original problem, there were sticks and squares as the "primary" elements but they labeled them "squares" and "sides" which worked for both the original pattern and their diamond pattern, however, when they work with the hexagon made up of triangles, they changed squares to "POLYHEDRA" and recorded that hexagons as "hexagon/w triangles". This is how the formula for the number of cubes in their piramid gets recorded in that textbox:
		+
		+	SIDES:
		+	square:
		+	N(N+3)
		+	diamond:
		+	(n^2+(n-1)^2)2+n3-2
		+	hexagon w/ triangles:
		+	9n(n+1)-6n
		+
		+
		+	POLYHEDRA:
		+	square
		+	n(n-1)/2
		+	diamond:
		+	n^2+(n-1)^2
		+	hexagon w/ triangles
		+	6n^2
		+	cubes in pyramid shape:
		+	f(n)=f(n-1)+x(X+1)/2
		+
		+
		+	Now that they are working with cubes, they can use, sticks, squares ("faces"), and cubes.

	===Like we said earlier===		===Like we said earlier===

Jsarmi: /* Usually.... */

Jsarmi — Sun, 04 May 2008 17:35:02 GMT

Usually....

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	Jason 5/18/06 7:41:35 PM EDT: i think that form is good		Jason 5/18/06 7:41:35 PM EDT: i think that form is good
	Jason 5/18/06 7:41:49 PM EDT: like we said earlier, recursiveness=easy to track pattern of growth		Jason 5/18/06 7:41:49 PM EDT: like we said earlier, recursiveness=easy to track pattern of growth
		+
		+	===Wouldn't this work?===
		+	OT points to his earlier posting indicating a reuse of something they did in last session on the hexagon:
		+
		+	137 5/18/06 7:41:52 PM EDT: Wouldn't this work? [Points to: I think we should just look at it in 3 groups of parallel lines like last time.]
		+	137 5/18/06 7:42:06 PM EDT: Each cube has 2 pointing each direction.
		+	137 5/18/06 7:42:11 PM EDT: Wait.
		+	137 5/18/06 7:42:13 PM EDT: 4.
		+	qwertyuiop 5/18/06 7:42:28 PM EDT: i think so [Points to: Wouldn't this work?]
		+	qwertyuiop 5/18/06 7:43:38 PM EDT: the overlap is different depending on wether the cube is on the outside of the shape or on the inside
		+
		+	Later QW makes a series of very interesting graphs that form a proposal for how to calculate the number of edges and posts:
		+
		+	qwertyuiop 5/18/06 8:02:49 PM EDT: so the first part of the equation would be 3 times the number of cubes
		+	qwertyuiop 5/18/06 8:03:12 PM EDT: I cn't think how to get the other part, though.
		+
		+	but unfortunately time runs out and the moderator closes the session with some questions.

	===Usually....===		===Usually....===

Jsarmi: /* Like we said earlier */

Jsarmi — Sun, 04 May 2008 17:03:56 GMT

Like we said earlier

←Older revision		Revision as of 17:03, 4 May 2008
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	...		...
	137 5/18/06 7:20:31 PM EDT: I think we should just look at it in 3 groups of parallel lines like last time.		137 5/18/06 7:20:31 PM EDT: I think we should just look at it in 3 groups of parallel lines like last time.
		+
		+	===Triangular numbers===
		+	Notice the reapearance of the definition of triangular numbers
		+
		+	Jason 5/18/06 7:26:29 PM EDT: can you get the next level for these cubes
		+	Jason 5/18/06 7:26:38 PM EDT: then we might be able to start seeing a pattern
		+	p M M M M M
		+	qwertyuiop 5/18/06 7:27:20 PM EDT: I think that's n=4.
		+	137 5/18/06 7:27:34 PM EDT: The number of cubes is the sum of n consecutive triangular numbers...
		+	qwertyuiop 5/18/06 7:27:49 PM EDT: triangular?
		+	qwertyuiop 5/18/06 7:27:49 PM EDT:
		+	Jason 5/18/06 7:27:57 PM EDT: woah
		+	Jason 5/18/06 7:28:15 PM EDT: (reacting to the diagram i mean)
		+	137 5/18/06 7:28:22 PM EDT: Numbers that are the sum of counstecutibe numbers starting from 1...
		+	Jason 5/18/06 7:28:43 PM EDT: how many cubes are in that diagram that you just posted?
		+	qwertyuiop 5/18/06 7:28:45 PM EDT: counstecutible?
		+	137 5/18/06 7:28:57 PM EDT: consecutive.
		+	137 5/18/06 7:29:07 PM EDT: Sry.
		+	qwertyuiop 5/18/06 7:29:09 PM EDT: 1 min
		+	137 5/18/06 7:29:34 PM EDT: 10+6+3+1=20.
		+

	===Like we said earlier===		===Like we said earlier===

Jsarmi: /* Session III */

Jsarmi — Sun, 04 May 2008 13:46:11 GMT

Session III

←Older revision		Revision as of 13:46, 4 May 2008
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	==Session III==		==Session III==
		+	Noticed that this session's feedback does not really contain any statements about things "you should have done different". A couple of suggestions for things to post on the wiki are followed up eventually but there is really no other direct discussion about the feedback. One could say that there is uptake because the suggestion of working on problems the group finds interesting is, indeed, what they do
		+
		+	===we do what we did last time again?===
		+
		+	137 5/16/06 7:04:41 PM EDT: So we do what we did last time again?
		+	nan 5/16/06 7:04:47 PM EDT: yes

	===Triangular Numbers===		===Triangular Numbers===
-	~~Something other teams discovered~~ but for which there is no group-to-group ~~interaction~~	+	137 creates a hexagonal grid on the whiteboard but it doesn't look too good so he asks somebody else to try it. QW does it:
		+
		+	qwertyuiop 5/16/06 7:14:51 PM EDT: triangles are done
		+	137 5/16/06 7:15:08 PM EDT: So do you want to first calculate the number of triangles in a hexagonal array?
		+
		+	They work on this grid for a while and come to the idea of triangular numbers. This is something that Team B also worked withbut for which there is no group-to-group exchange. First both QW and 137 make references to things they had contributed in the previous session: "each polygon corrisponds to 2 sides" and the 1-3-5 pattern. Only QW does it explicitly with a reference to LAST TIME and quotes:
		+
		+	Jason 5/16/06 7:20:02 PM EDT: so... should we try to find a formula i guess
		+	Jason 5/16/06 7:20:22 PM EDT: input: side length; output: # triangles
		+	qwertyuiop 5/16/06 7:20:39 PM EDT: It might be easier to see it as the 6 smaller triangles.
		+	137 5/16/06 7:20:48 PM EDT: Like this?
		+	p M M M
		+	qwertyuiop 5/16/06 7:21:02 PM EDT: yes
		+	Jason 5/16/06 7:21:03 PM EDT: yup
		+	p M M
		+	qwertyuiop 5/16/06 7:21:29 PM EDT: side length is the same...
		+	Jason 5/16/06 7:22:06 PM EDT: yeah
		+	Jason 5/16/06 7:22:13 PM EDT: so it'll just be x6 for # triangles in the hexagon
		+	137 5/16/06 7:22:19 PM EDT: Each one has 1+3+5 triangles.
		+	Jason 5/16/06 7:22:23 PM EDT: but then we're assuming just regular hexagons
		+	qwertyuiop 5/16/06 7:22:29 PM EDT: the "each polygon corrisponds to 2 sides" thing we did last time doesn't work for triangles
		+
		+
		+	later 137 proposes a formula and JS offers support with an objection:
		+
		+	137 5/16/06 7:24:49 PM EDT: And there are n terms so... n(2n/2)
		+	137 5/16/06 7:25:07 PM EDT: or n^2
		+	Jason 5/16/06 7:25:17 PM EDT: yeah
		+	Jason 5/16/06 7:25:21 PM EDT: then multiply by 6
		+	137 5/16/06 7:25:31 PM EDT: To get 6n^2
		+	Jason 5/16/06 7:25:39 PM EDT: but this is only with regular hexagons... is it possible to have one
		+	definite formula for irregular hexagons as well
		+
		+
		+	So they do some more work and triangular numbers emerge

	qwertyuiop 5/16/06 7:33:54 PM EDT: I don't see the pattern yet...		qwertyuiop 5/16/06 7:33:54 PM EDT: I don't see the pattern yet...
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	137 leaves the room 5/16/06 8:24:28 PM EDT		137 leaves the room 5/16/06 8:24:28 PM EDT
	qwertyuiop 5/16/06 8:25:02 PM EDT: i'll write it.		qwertyuiop 5/16/06 8:25:02 PM EDT: i'll write it.
-

	==Feedback III==		==Feedback III==

Jsarmi: /* The "each square with 2 sides" thing doesn't work as neatly here */

Jsarmi — Sat, 03 May 2008 22:16:38 GMT

The "each square with 2 sides" thing doesn't work as neatly here

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	Jason 5/11/06 7:54:13 PM EDT: if we look at rows, its 1, 3, 5, 3, 1		Jason 5/11/06 7:54:13 PM EDT: if we look at rows, its 1, 3, 5, 3, 1

		+	===How did you get that===
		+	This is the third "how did you get that" of the session. It required a second call for an uptake.

		+	qwertyuiop 5/11/06 7:54:28 PM EDT: how did you get that?
		+	Jason 5/11/06 7:54:29 PM EDT: by side length you mean...
		+	p M M M
		+	137 5/11/06 7:54:50 PM EDT: The orange.
		+	(...)
		+	Jason 5/11/06 7:55:52 PM EDT: can you explain how you got that formula?
		+
		+	137 attempts a number of diagrams but seems to have trouble with coloring. Later QW posts a formula for Number of sides. Jason rembers that 137 had posted a formula earlier and points to it (this one)
		+
		+	qwertyuiop 5/11/06 8:00:57 PM EDT: i think NumberOfSides=NumberOfSquares2+SideLength3-2
		+	p M M
		+	Jason 5/11/06 8:01:29 PM EDT: wait-- you gave a formula earlier
		+	p M
		+	Jason 5/11/06 8:01:34 PM EDT: lemme see if i can find it
		+	p M
		+	qwertyuiop 5/11/06 8:01:42 PM EDT: because it's like the first shape, but with 3 other edges
		+	p M
		+	Jason 5/11/06 8:01:55 PM EDT: this one
		+	p M M M M M M
		+	Jason 5/11/06 8:02:12 PM EDT: oh but you're talking about # of sides
		+
		+	later with more diagrams, 137 posts that "he screwed up somewhere" and Jason makes another observation:
		+
		+	Jason 5/11/06 8:08:18 PM EDT: 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
		+	Jason 5/11/06 8:08:35 PM EDT: just a thought... not sure if it'll work
		+
		+	Then QW makes a proposal "using your previous method" which they agree works:
		+
		+	qwertyuiop 5/11/06 8:08:35 PM EDT: using your previous method: SideLenght^2 + (SideLength-1)^2
		+	qwertyuiop 5/11/06 8:08:51 PM EDT: does that work?
		+	qwertyuiop 5/11/06 8:10:06 PM EDT: the part in front of the plus is the large, rotatewd 45 square and
		+	the part after it is the smaller, not rotated squared
		+	qwertyuiop 5/11/06 8:10:59 PM EDT: um... hello?
		+	137 5/11/06 8:11:03 PM EDT: Hi.
		+	Jason 5/11/06 8:11:17 PM EDT: well, looking at the center diagram with the orange boxed
		+	qwertyuiop 5/11/06 8:11:18 PM EDT: but does that work?
		+	Jason 5/11/06 8:11:20 PM EDT: boxes
		+	Jason 5/11/06 8:11:24 PM EDT: you'd be 1 off
		+	Jason 5/11/06 8:11:41 PM EDT: nvm, my arithmetic skills faltered ther
		+	Jason 5/11/06 8:11:42 PM EDT: e
		+	p M M
		+	Jason 5/11/06 8:11:59 PM EDT: there
		+	qwertyuiop 5/11/06 8:12:03 PM EDT: checking for SideLenght=3...
		+	Jason 5/11/06 8:12:35 PM EDT: works
		+	qwertyuiop 5/11/06 8:12:36 PM EDT: yes, it works
		+	Jason 5/11/06 8:12:52 PM EDT: cool, so should we call this a formula
		+
		+	And the forth "how do you get it" of the session:
		+
		+	137 5/11/06 8:12:57 PM EDT: I don't get why though...
		+	Jason 5/11/06 8:13:29 PM EDT: i dont either
		+	p M M M M
		+	qwertyuiop 5/11/06 8:14:10 PM EDT: I used your previous method: take the (orange) side; that^2 gives part of the shape...
		+	qwertyuiop 5/11/06 8:15:03 PM EDT: the rest happens to be a square with a side length of one less, therfore th "(SideLength-1)^2"
		+	qwertyuiop 5/11/06 8:15:10 PM EDT: does that make sense?
		+	Jason 5/11/06 8:15:42 PM EDT: i get it!
		+	Jason 5/11/06 8:15:43 PM EDT: clever :)
		+	qwertyuiop 5/11/06 8:15:48 PM EDT: 137?
		+	137 5/11/06 8:15:56 PM EDT: Now I do.
		+
		+	===3D but time runs out===
		+	and the moderator suggests working on the Wiki
		+
		+	qwertyuiop 5/11/06 8:22:40 PM EDT: to make it more 3D, you could continue the pattern along the new dimension
		+	qwertyuiop 5/11/06 8:22:57 PM EDT: not sure how you would draw that...
		+	Jason 5/11/06 8:23:38 PM EDT: well going back to our session problems
		+	Jason 5/11/06 8:23:38 PM EDT: What are the different methods (induction, series, recursion, graphing, tables, etc.) you can use to analye these different patterns?
		+	Jason 5/11/06 8:23:57 PM EDT: i'd say series (recursive or explicit) for many of them
		+	Jason 5/11/06 8:24:49 PM EDT: anyone else?
		+	qwertyuiop 5/11/06 8:24:59 PM EDT: induction?
		+	Jason 5/11/06 8:25:58 PM EDT: what's that
		+	...
		+
		+	Notice "last time" but no incidence in problem solving
		+
		+	Cynthia 5/11/06 8:26:13 PM EDT: so i'm wondering if this is a good time to figure out the information that you are going to post to the wiki?
		+	Jason 5/11/06 8:26:30 PM EDT: hmm
		+	qwertyuiop 5/11/06 8:26:30 PM EDT: the equations...
		+	Jason 5/11/06 8:26:55 PM EDT: 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
		+	qwertyuiop 5/11/06 8:28:25 PM EDT: there are 4, I think: number of squares and number of sides for both diamonds and the first problem
		+	Jason 5/11/06 8:28:47 PM EDT: alright
		+	Jason 5/11/06 8:29:05 PM EDT: 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
		+	qwertyuiop 5/11/06 8:29:35 PM EDT: we could just do it here
		+	Jason 5/11/06 8:29:47 PM EDT: do what here
		+	qwertyuiop 5/11/06 8:29:59 PM EDT: write it

	==Feedback II==		==Feedback II==

Jsarmi: /* Other problems to do? */

Jsarmi — Sat, 03 May 2008 21:33:57 GMT

Jsarmi: /* What do we do now? */

Jsarmi — Sat, 03 May 2008 21:33:30 GMT

What do we do now?

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	Jason 5/11/06 7:54:13 PM EDT: if we look at rows, its 1, 3, 5, 3, 1		Jason 5/11/06 7:54:13 PM EDT: if we look at rows, its 1, 3, 5, 3, 1

-	~~===What do we do now?===~~

-	~~137 5/11/06 7:48:12 PM EDT: Er... Am I lagging or is nobody typing?~~
-	~~qwertyuiop 5/11/06 7:48:21 PM EDT: nobody is typing~~
-	~~Jason 5/11/06 7:48:21 PM EDT: typing now :)~~
-	~~qwertyuiop 5/11/06 7:48:37 PM EDT: are there other problems to do?~~
-	~~137 5/11/06 7:48:51 PM EDT: I do not think so...~~
-	~~Jason 5/11/06 7:48:58 PM EDT: well~~
-	~~Jason 5/11/06 7:49:03 PM EDT: we are supposed to come up with some~~
-	~~qwertyuiop 5/11/06 7:49:10 PM EDT: ok...~~
-	~~Cynthia 5/11/06 7:49:13 PM EDT: did you view the topic for tonight, session 2~~
-	~~Jason 5/11/06 7:49:17 PM EDT: 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?~~
-	~~Cynthia 5/11/06 7:49:45 PM EDT: thanks, jason~~
-	~~137 5/11/06 7:50:07 PM EDT: Let's try diamonds first..~~
-	~~p M~~
-	~~Jason 5/11/06 7:50:17 PM EDT: ok~~
-	~~p M M~~
-	~~Jason 5/11/06 7:50:27 PM EDT: if the squares were arranged in a diamond-like shape...~~
-	~~p M M M M~~
-	~~Jason 5/11/06 7:50:37 PM EDT: wait -- lemme make sure i read the directions carefully~~

	==Feedback II==		==Feedback II==

Jsarmi: /* The "each square with 2 sides" thing doesn't work as neatly here */

Jsarmi — Sat, 03 May 2008 21:32:09 GMT

The "each square with 2 sides" thing doesn't work as neatly here

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	===The "each square with 2 sides" thing doesn't work as neatly here===		===The "each square with 2 sides" thing doesn't work as neatly here===
		+	This is something that QW had said earlier when speaking about "overlap" ( qwertyuiop 5/11/06 7:39:02 PM EDT: 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)

	Jason 5/11/06 7:53:52 PM EDT: ok		Jason 5/11/06 7:53:52 PM EDT: ok

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	qwertyuiop 5/11/06 7:49:10 PM EDT: ok...		qwertyuiop 5/11/06 7:49:10 PM EDT: ok...
	Cynthia 5/11/06 7:49:13 PM EDT: did you view the topic for tonight, session 2		Cynthia 5/11/06 7:49:13 PM EDT: did you view the topic for tonight, session 2
-	Jason 5/11/06 7:49:17 PM EDT: WHAT IF? Mathematicians do not just solve other people's problems - they also explore little	+	Jason 5/11/06 7:49:17 PM EDT: WHAT IF? Mathematicians do not just solve other people's problems - they also explore little worlds
-	worlds of patterns that they define and find interesting. Think about other mathematical problems...	+	of patterns that they define and find interesting. Think about other mathematical problems related to the problem with the sticks.
-	(Taken from the topic)	+	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?
		+	--->(Taken from the topic)
	Cynthia 5/11/06 7:49:45 PM EDT: thanks, jason		Cynthia 5/11/06 7:49:45 PM EDT: thanks, jason
	137 5/11/06 7:50:07 PM EDT: Let's try diamonds first..		137 5/11/06 7:50:07 PM EDT: Let's try diamonds first..