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Walking Around the World


Date: 08/18/99 at 11:22:03
From: Billy
Subject: Geometry

A man walks around the world. How much farther does his head go than 
his feet? It has to be the same, right? If you walk to the moon your 
head will travel the same distance. Is this a trick question?


Date: 08/18/99 at 11:58:52
From: Doctor Peterson
Subject: Re: Geometry

Hi, Billy.

No, it's not a trick question, but you have to think carefully. If you 
walk in a straight line, your head goes as far as your feet, but not 
if you walk in a circle. Here's a man walking around the world:

                    .....O.....
               .....    /|\    .....
            ...          |          ....
         ...            / \             ..
       ..           ***********           ..
      .         ****     |     ****         .
     .        **         |         **        .
    .       **           |           **       .
   .       *             |             *       .
   .      *              |              *      .
  .      *               |               *      .
  .      *               +---------------*------.
  .      *                       r       *   h  .
   .      *                             *      .
   .       *                           *       .
    .       **                       **       .
     .        **                   **        .
      .         ****           ****         .
       ..           ***********           ..
         ...                            ..
            ...                     ....
               .....           .....
                    ...........

His feet walk around the circumference of a circle with radius r. His 
head goes around a circle with radius r+h. See if you can figure out 
how much farther that is!

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
Middle School Conic Sections/Circles
Middle School Geometry

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