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Thread: What is the Shortest Path?

20041229, 01:33 #1
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What is the Shortest Path?
Imagine an open box that is 2.2 units wide, 5.5 Units long and 1.1 units tall.
An ant stands at the top corner labled "S".
The ant knows that if he were a fly, that he could fly the 6.02 units to the opposite inner corner (Labeled "E").
Being only an ant, he must walk (along the top sides, walls, bottom, etc) from Point "S" to Point "E".
If the ant takes the shortest route, how far must he travel?
Steve

20041229, 01:55 #2
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Re: What is the Shortest Path?
I thought this was easy, so what is wrong with this calculation...
If you <span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">open the box out so that it becomes a 2D net for a box</span hide> then you can see that the distance is <span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">the hypoteneuse of a right angled triangle with other sides of 5.5+1.1 and 2.2 (and also a different triangle of sides 2.2 + 1.1 and 5.5). The first one works out as SQRT(6.6 * 6.6 + 2.2 * 2.2) = SQRT (43.56+4.84) which my calculator says is about 7.208; the other triangle seems to give me a value of 6.414.</span hide>
StuartR

20041229, 01:59 #3
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Re: What is the Shortest Path?
<span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">Flatten the box. The shortest route must be a straight line. There are two possibilities: the square root of (5.5+1.1)^2 + 2.2^2 ~ 6.96, or the square root of 5.5^2 + (2.2+1.1)^2 ~ 6.41. The latter is shorter, so that is the answer (1.1 * SQRT(34) for people liking mathematical solutions)</span hide>

20041229, 02:04 #4
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Re: What is the Shortest Path?
I figured the same as your first method, but my calculator gives <span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">6.957</span hide>.
Alan

20041229, 02:06 #5
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Re: What is the Shortest Path?
I might have beaten Hans by a few seconds, but I missed the point that <span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">the two lines are different lengths, so you have to calculate both and choose the shortest.</span hide>
See diagram attached.
StuartR

20041229, 03:12 #6
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Re: What is the Shortest Path?
I will give it to you. You gave the shortest path and an indication of how to get it (and you beat Hans to the answer <img src=/S/smile.gif border=0 alt=smile width=15 height=15>)
Steve

20041229, 09:21 #7
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Re: What is the Shortest Path?
Celebratory drinks for me tonight then.
StuartR