You have a 'hallway' in 2 dimension, length between walls is one unit. Suppose there is a 'corner' in this hallway, i.e. both walls make a perfect 90 degree angle and then continue on with distance between them still one unit. What is the maximum area 2d shape that could go the entire length of this hallway (including the turn) without ever going through any walls? The shape is only allowed to 'slide' or 'rotate' in 2 dimensions. obviously no deforming allowed.
2007-03-21 22:20:43 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
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Its just the bigest area shape that can get from A to B. obviously a 1 by 1 square can do it, thats area 1, but u can get a lot more area than that. what is maximum?
2007-03-21 22:44:50 · update #1
huh! the diagram didnt come out correctly haha, its just a silly hall with a 90 degree corner easy to visualize.
2007-03-21 22:46:08 · update #2
of course a circle with diameter greater than 1 cannot enter the hallyway without knocking down some walls, for example.
2007-03-21 22:50:57 · update #3
I saw this problem many years ago. I seem to remember that the solution is something like a dumbell or two shapes connected by a thin rod. I think that the shapes were squares with opposite corners rounded off.
2007-03-22 04:21:16 · answer #1 · answered by Anonymous · 0⤊ 0⤋
I believe that the maximum area is 1 square unit.
If the shape is not going to turn, then it can be a square of width 1. This is the max.
If the shape is going to turn through 90° as it goes around the corner, then it should be a rectangle. The rectangle with maximum area is 1/sqrt(2) wide and sqrt(2) long. This also has an area of 1 square unit.
I worked this out using calculus but it is hard to include the diagram here.
2007-03-22 05:58:18 · answer #2 · answered by Gnomon 6 · 0⤊ 0⤋
If I understand you right.
If you walk along the hall and come to a corner, and then at that moment the hall moves direction by 90°, you can walk along the next side of the hall until you come to the next corner. If this process continues to repeat, then you could walk forever, or have an eternal distance.
2007-03-22 05:34:10 · answer #3 · answered by Brenmore 5 · 0⤊ 1⤋
max lenght that can pass=(2^1/2)
for maximum area the 2d figure should be a circle with above lenght as diameter
area=(pi)d^2/4=pi*2/4=pi/2
2007-03-22 05:34:24 · answer #4 · answered by tarundeep300 3 · 0⤊ 1⤋
Max length = 2*sqt(2)
2007-03-22 05:25:21 · answer #5 · answered by blighmaster 3 · 0⤊ 1⤋
it is a solutionless problem.
This figure is not possible.
Please send me a diagram of this question (what you think it should be) to ds_mik@yahoo.com
2007-03-22 05:35:28 · answer #6 · answered by Anonymous · 0⤊ 1⤋
???
2007-03-22 06:08:55 · answer #7 · answered by jopescu 2 · 0⤊ 0⤋