Dataset1/D1T2S3n
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Moderator works on continuity
Moderator_G 5/17/05 7:37:19 PM EDT: I was curious about your formula for the number of shortest paths
bob123 5/17/05 7:37:36 PM EDT: it's pascal's triangle
Moderator_G 5/17/05 7:37:53 PM EDT: Oh!
Moderator_G 5/17/05 7:38:22 PM EDT: why would that be the number of shortest paths?
Moderator_G 5/17/05 7:41:31 PM EDT: It did seem to work for the examples you tried
Moderator_G 5/17/05 7:41:48 PM EDT: But I did not understand how you thought it up
bob123 5/17/05 7:43:03 PM EDT: draw a rectangle
bob123 5/17/05 7:43:07 PM EDT: and label it with numbers
bob123 5/17/05 7:43:27 PM EDT: for the number of ways to get there
bob123 5/17/05 7:43:46 PM EDT: starting from the top right corner and ending at the lower left corner
bob123 5/17/05 7:43:49 PM EDT: the top right corner is 1
bob123 5/17/05 7:44:53 PM EDT: then the rest, you just add the numbers of the two vertices that are next to it
(the one on the right of it and the one on top of it)
Moderator_G 5/17/05 7:46:14 PM EDT: Whoa, Bob. You are going too fast for me. Let's wait for the others to show up.
bob123 5/17/05 7:47:09 PM EDT: ok
Moderator_G 5/17/05 7:52:10 PM EDT: Bob, Where did you learn about Pascal's triangle?
...
qwer 5/17/05 7:55:57 PM EDT: hi
bob123 5/17/05 7:56:13 PM EDT: hi
Moderator_G 5/17/05 7:56:42 PM EDT: Hi everyone
qwer 5/17/05 7:56:54 PM EDT: What's Pascal's triangle?
Moderator_G 5/17/05 7:57:30 PM EDT: Bob and I started talking about his formula last time.
Moderator_G 5/17/05 7:57:47 PM EDT: Can you see our messages?
qwer 5/17/05 7:57:54 PM EDT: Yes
...
qwer 5/17/05 8:03:54 PM EDT: I just found a description of the triangle at http://mathworld.wolfram.com/PascalsTriangle.html
The problem is, I don't remember my formula
bob123 5/17/05 8:04:07 PM EDT: the problem is bob123 5/17/05 8:04:17 PM EDT: i'm not too sure what the formula i made up last week is mathisfun 5/17/05 8:04:34 PM EDT: then how u get it? bob123 5/17/05 8:04:51 PM EDT: i got it bob123 5/17/05 8:04:55 PM EDT: but then i forgot it bob123 5/17/05 8:05:00 PM EDT: give me 5 minutes to reget it bob123 5/17/05 8:05:14 PM EDT: i have short term memory loss bob123 5/17/05 8:06:09 PM EDT: ok bob123 5/17/05 8:06:10 PM EDT: there bob123 5/17/05 8:06:14 PM EDT: i remember how i got it now bob123 5/17/05 8:06:43 PM EDT: or do i... bob123 5/17/05 8:07:21 PM EDT: there we go on the whiteboard: In an n by m rectangle (n>m), the number of ways to get from the top left corner to the bottom right corner without retracing steps or going backwards (where going backwards is defined as making a move such that it would result in making the distance between the point and the top left corner shorter) is: (m+n) choose (m) or (m+n) choose (n) or (m+n)!/(m!n!)
Where is the other guy?
bob123 5/17/05 8:08:35 PM EDT: where's the other guy? bob123 5/17/05 8:08:45 PM EDT: the SithLordVader or something guy
Summarize to a newcommer
Moderator_G 5/17/05 8:16:47 PM EDT: Can someone explain to theyypu234 what you found about the grid?
qwer 5/17/05 8:17:56 PM EDT: In the yellow box bellow the grid is a formula for how many shortest distances
there are from one point on a grid to another, staying on the lines of the grid.
Moderator's questions...
Moderator_G 5/17/05 8:19:36 PM EDT: During the first two sessions of this program the groups have at times
explored a math where points only exist at the intersections of a grid (this one is 12 lines by 12
lines), evenly spaced one unit apart as in the image on the whiteboard. There are no "diagonal"
lines, at least not in the way we usually think of them.
Moderator_G 5/17/05 8:19:53 PM EDT: Distance between any two points in this grid world is defined as the length of the shortest path
along the grid lines connecting the points. Several groups showed there may be several shortest
paths, but the distance is well-defined. This is a system of math that you are inventing, just as
the Greeks invented geometry.
Moderator_G 5/17/05 8:20:09 PM EDT: Did anyone think of any other questions after the last session?
bob123 5/17/05 8:20:14 PM EDT: oh, i only got a 3 on my AIME, my index was like 25.7 (barely made B, :))
bob123 5/17/05 8:20:20 PM EDT: umm
mathisfun 5/17/05 8:20:32 PM EDT: still thinking about the last question...
qwer 5/17/05 8:20:35 PM EDT: Yes, but I forgot it.
mathisfun 5/17/05 8:20:54 PM EDT: the one about the cylinder or a flat surface one
bob123 5/17/05 8:20:58 PM EDT: oh
bob123 5/17/05 8:21:37 PM EDT: i think i get that one now
Moderator_G 5/17/05 8:21:53 PM EDT: I put some questionsin the yellow box that come up when looking at your work.
You don't need to pay any attention to these if you don't want to. Again, your goal is to identify
or invent new math questions that are interesting to you and pursue them.
mathisfun 5/17/05 8:21:55 PM EDT: so do u still think it is a cylinder?]
There was a question last time, on Thursday
mathisfun 5/17/05 8:21:55 PM EDT: so do u still think it is a cylinder?] qwer 5/17/05 8:22:10 PM EDT: think what is? bob123 5/17/05 8:22:21 PM EDT: i know it's a cylinder mathisfun 5/17/05 8:22:30 PM EDT: there wsa a question last time on Thursday remember? qwer 5/17/05 8:23:19 PM EDT: Which one? mathisfun 5/17/05 8:23:41 PM EDT: the one where the paper wsa folded and then we find the distance qwer 5/17/05 8:23:51 PM EDT: Yes. bob123 5/17/05 8:23:54 PM EDT: yep, i get it now mathisfun 5/17/05 8:23:57 PM EDT: (the paper was folded in half) mathisfun 5/17/05 8:24:04 PM EDT: K i'll make a cylinder bob123 5/17/05 8:24:07 PM EDT: think right triangles bob123 5/17/05 8:24:15 PM EDT: and circumference of base circle bob123 5/17/05 8:24:51 PM EDT: finding the distance would involve the law of cosines, but that's ok
Plans and Reflections?
Moderator_G 5/17/05 9:03:21 PM EDT: What did you conclude about the cylinder? mathisfun 5/17/05 9:04:00 PM EDT: it was an interesting problem mathisfun 5/17/05 9:04:17 PM EDT: thinking about it really helped Moderator_G 5/17/05 9:04:40 PM EDT: did talking about it with others help? mathisfun 5/17/05 9:04:53 PM EDT: yeah qwer 5/17/05 9:04:58 PM EDT: yes Moderator_G 5/17/05 9:05:22 PM EDT: what do you want to do next time? qwer 5/17/05 9:05:53 PM EDT: mabey use points on another shape mathisfun 5/17/05 9:06:18 PM EDT: fold the shape into thirds... mathisfun 5/17/05 9:06:37 PM EDT: or we can work on the new problems given Moderator_G 5/17/05 9:07:20 PM EDT: Anything else? Moderator_G 5/17/05 9:07:44 PM EDT: Think about what you want to do between now and Thursday mathisfun 5/17/05 9:07:52 PM EDT: alright
