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James King
Posts:
66
From:
University of Washington
Registered:
12/3/04


Re: Volume of pyramid
Posted:
Jan 29, 1993 12:01 AM


In article <1993Jan22.143853.23359@sophia.smith.edu> Joseph O'Rourke, orourke@sophia.smith.edu writes: >MessageID: <1993Jan22.143633.23253@sophia.smith.edu>
In article <1993Jan22.143853.23359@sophia.smith.edu> Joseph O'Rourke, orourke@sophia.smith.edu writes: >MessageID: <1993Jan22.143633.23253@sophia.smith.edu>
One way of visualizing the decomposition of a cube into three congruent pyramids with square bases is to think of a light in the corner of a cubical room. Then the light rays will only intersect three of the sides of the cube (not counting the ones contained in the three sides that are adjacent to the light). The union of all the rays that hit one of the 3 opposite sides is a pyramid.
As it happens, I demonstrated this in my geometry class on Wednesday by bringing in a cardboard box and cutting it apart with a utility knife. I don't know whether the students were impressed by the mathematics but they were hold their breath to see if I would slice myself instead of the box!
When you think of the visualization this way, you can easily see the twodimensional analog (a square cut into 2 triangles) and the fourdimensional analog.
Jim King



