Minimum DistanceDate: 22 May 1995 22:29:15 -0400 From: Lew England Subject: Finding Minimum Distance To whom it may concern: I am preparing to give a multimedia presentation concerning the Internet and Education to a large group of teachers, students, and parents. I hoped you could answer the following question so I could provide an example when I refer students to your program. This was taken from a school geometry book: "Inside a rectangular room, measuring 30' in length and 12' in width and height, a spider is at a point on the middle of one of the end walls, 1 foot from the ceiling, as shown at A; and a fly is on the opposite wall, 1 foot from the floor in the center, as shown at B. What is the shortest distance that the spider must crawl in order to reach the fly, which remains stationary? Of course the spider never drops or uses its web, but crawls fairly." Thank you for your consideration. Sincerely, Bob England P.S. I have also provided an example in GIF format. Date: 23 May 1995 00:45:08 -0400 From: Dr. Ken Subject: Finding Minimum Distance Hello there! I'm glad to hear about your upcoming presentation, and I hope it goes well. The trick to this problem is realizing that you can cut the spider's box open and lay it flat. Then the problem becomes an exercise in good old plane geometry. Here are three different ways you could lay the box out, where the x is the spider and the o is the fly: 12 30 12 ----------------------------------------------- | | | | | | | | | x| | o| 12 | | | | | | | | ----------------------------------------------- | | | | | | | | | | ------------------------------- | | | | | | | | | | ------------------------------- | | | | | | | | | | ------------------------------- 12 30 --------------------------------------- | | | | | | | x| | | | | | | | 12 ----------------------------------------------- | | | | | | | | | 12 | | | | | o | --------------------------------------- | | | | | | | | | | ------------------------------- | | | | | | | | | | ------------------------------- 12 30 --------------------------------------- | | | | | | | x| | | | | | | | --------------------------------------- | | | | | | | | | | 12 --------------------------------------- | | | | | | | |o | 12 | | | | | | --------------------------------------- | | | | | | | | | | ------------------------------- Whew! Laying the boxes out this way, it is pretty clear that our only options for the spider's shortest paths are the ones that we make by connecting the spider and the fly via a straight line in these diagrams. The problem then becomes an exercise in the Pythagorean theorem to find the three distances, and then comparing them to see which is the shortest. I'll let you take it from here, and if you have any questions, don't hesitate to write back! -K |
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