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Ch 1, shortest path when there are two lines

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  • shannon Stoney
    I am having a hard time understanding why you solve the problems involving two lines (in the projects) by drawing a line from A* to B*. That was not my first
    Message 1 of 2 , Jan 5, 2013
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      I am having a hard time understanding why you solve the problems involving two lines (in the projects) by drawing a line from A* to B*. That was not my first guess, and I still don't see why that works.

      Any hints?

      --shannon
    • David Chandler
      Get two flat mirrors. Place them vertically on a table with reflective sides toward each other. Place two raisins or other small objects between the mirrors.
      Message 2 of 2 , Jan 5, 2013
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        Get two flat mirrors.  Place them vertically on a table with reflective sides toward each other.  Place two raisins or other small objects between the mirrors.  You should see various raisins, counting all the mirror images of raisins.  You should also see mirror images of the mirrors.  If you connect any two raisin images, there is a corresponding path between the two actual raisins that bounces around between the two actual mirrors.  (The Geometer's Sketchpad demos for the Project Section illustrates this.)  This is an extension of the insight that led to the solution of the original problem in the Central Section.
        --David Chandler


        On Sat, Jan 5, 2013 at 1:16 PM, shannon Stoney <shannonstoney@...> wrote:
         

        I am having a hard time understanding why you solve the problems involving two lines (in the projects) by drawing a line from A* to B*. That was not my first guess, and I still don't see why that works.

        Any hints?

        --shannon


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