Dataset1/D1T2S2n
From Jsarmi
< Dataset1
Remember what you were doing?
Moderator_G 5/12/05 7:57:50 PM EDT: Remember what you were doing Tuesday?
mathisfun 5/12/05 7:57:56 PM EDT: sorta
qwer 5/12/05 7:57:57 PM EDT: Yes.
Moderator_G 5/12/05 7:58:04 PM EDT: What?
mathisfun 5/12/05 7:58:13 PM EDT: i'm pretty sure
qwer 5/12/05 7:58:55 PM EDT: There were two points on a grid in which one could only travel on the lines and
we made and answerd questions about it.
Moderator_G 5/12/05 7:59:56 PM EDT: Right. There were several groups like yours and they each came up
with several ideas about this grid world
Moderator_G 5/12/05 8:00:11 PM EDT: I listed some of their questions ...
Moderator_G 5/12/05 8:00:41 PM EDT: ... and also some questions that these group questions raised for the moderators
Moderator_G 5/12/05 8:01:04 PM EDT: What do you think of these questions?
On the whiteboard:
Pretend you live in a world where you can only travel on the lines of the grid. You can't cut across a block on the diagonal, for instance. How does this change the math?
Questions from the groups: 1. What is the shortest path along the grid between the two points? 2. How many possible routes are there from point A to point B? 3. What is the maximum distance from point A to B if you can only travel on each POINT once? 4. How many ways are there to get from A to B in rectangle ABCD? 5. Make a right triangle with AB as the hypotenuse. What is the area of the circumscribed circle? 6. Can you go off the edge and come back somewhere else? Questions these raised for the moderators: 7. What is the shortest path along the grid between any two points A(x1, y1), B(x2, y2)? 8. How many shortest paths are there from A to B and how does this vary with changes in the positioning of A relative to B? 9. Suppose the right and left edges of the grid are connected. How does that change the distances between points?
mathisfun 5/12/05 8:05:48 PM EDT: though we already discuss the 8th with number 4 we this one uses more thinker involved
Newcomer goes for diagonal others correct her: WE are going along the lines
Marisol 5/12/05 8:18:49 PM EDT: for 7, the shortest way is the square root of [(x2-x1)**2 + (y2-y1)**2] bob123 5/12/05 8:19:27 PM EDT: but that wouldn't be along the grid qwer 5/12/05 8:19:39 PM EDT: or absolute vale, instead of using squares. mathisfun 5/12/05 8:19:51 PM EDT: We are going along the lines of the grid no diagonals allowed Marisol 5/12/05 8:20:12 PM EDT: O.K
Recorder role is "remembered" Original recorder is not present, somebody else takes over
mathisfun 5/12/05 8:21:16 PM EDT: who want to write that down? qwer 5/12/05 8:21:27 PM EDT: I will. mathisfun 5/12/05 8:21:30 PM EDT: k
We already did that yesterday, here it is (Formula reappears), try it, no need, I am not so sure
bob123 5/12/05 8:22:36 PM EDT: we already did that yesterday qwer 5/12/05 8:22:53 PM EDT: we did? mathisfun 5/12/05 8:23:02 PM EDT: but we did it so that there was only right and down bob123 5/12/05 8:23:07 PM EDT: i mean tuesday mathisfun 5/12/05 8:23:35 PM EDT: i guess we will do it with left and up? qwer 5/12/05 8:24:03 PM EDT: It would be almost the same. bob123 5/12/05 8:24:05 PM EDT: it's (|x2-x1|+|y2-y1|-2) choose (|x2-x1|-1) bob123 5/12/05 8:24:12 PM EDT: try it if you like mathisfun 5/12/05 8:24:17 PM EDT: nah mathisfun 5/12/05 8:24:25 PM EDT: if you are so sure... bob123 5/12/05 8:25:36 PM EDT: i'm not bob123 5/12/05 8:25:39 PM EDT: actually bob123 5/12/05 8:25:45 PM EDT: take out the -2 and the -1 mathisfun 5/12/05 8:25:59 PM EDT: then letz check it ...
Difficulties in Indexing common referent: right, down, down, or down, down, right, right, righ
mathisfun 5/12/05 8:28:44 PM EDT: is the one by two going to be 4 ways?
qwer 5/12/05 8:29:26 PM EDT: Can't you go, from A, right, down, right down, right, or right, right,
right, down, down, or down, down, right, right, right...
mathisfun 5/12/05 8:29:48 PM EDT: for which one?
qwer 5/12/05 8:30:01 PM EDT: #8
mathisfun 5/12/05 8:30:12 PM EDT: which shape?
qwer 5/12/05 8:30:41 PM EDT: the two points labled A and B
mathisfun 5/12/05 8:30:51 PM EDT: its one by one
qwer 5/12/05 8:31:14 PM EDT: On my screen it looks like 2x3.
mathisfun 5/12/05 8:31:24 PM EDT: are u at 100%?
qwer 5/12/05 8:31:42 PM EDT: Never mind. It changed.
mathisfun 5/12/05 8:31:51 PM EDT: good
Work on Qwer's past suggestion: reimman holes?
mathisfun 5/12/05 8:38:24 PM EDT: so lets work on number nine qwer 5/12/05 8:38:45 PM EDT: It makes the plane into a cylender. mathisfun 5/12/05 8:39:45 PM EDT: wait it a cylinder or a flat plane that is down mathisfun 5/12/05 8:39:56 PM EDT: (cut into half)? qwer 5/12/05 8:40:37 PM EDT: I imagine both sides wrapping around and connecting in the back.
Marison reapears later reinforcing the grid rule in a different context: 3D
Marisol 5/12/05 8:49:16 PM EDT: but wouldn't you have to follow the curved surface
I am bored
bob123 5/12/05 8:52:00 PM EDT: i'm bored
A plan for Next Tuesday
Marisol 5/12/05 9:00:11 PM EDT: Moderator, what is your opinion on #9 Moderator_G 5/12/05 9:00:56 PM EDT: I will think more about it between now and Tuesday. Marisol 5/12/05 9:01:30 PM EDT: k Moderator_G 5/12/05 9:01:53 PM EDT: I also found your solution of 8 very creative. I do not understand how you got it or why it works qwer 5/12/05 9:02:08 PM EDT: Neither do I. mathisfun 5/12/05 9:02:43 PM EDT: I was something that bob found out mathisfun 5/12/05 9:02:54 PM EDT: I guess we should ask him next time... mathisfun 5/12/05 9:03:00 PM EDT: or unless he responds Moderator_G 5/12/05 9:03:31 PM EDT: Maybe we can all think about it some more ... and make sure it really works Moderator_G 5/12/05 9:04:09 PM EDT: See you on Tuesday!
