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Topic: Volume of a Pyramid
Replies: 4   Last Post: Jan 29, 1993 12:01 AM

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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
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In article <1993Jan22.143853.23359@sophia.smith.edu> Joseph O'Rourke,
orourke@sophia.smith.edu writes:
>Message-ID: <1993Jan22.143633.23253@sophia.smith.edu>

In article <1993Jan22.143853.23359@sophia.smith.edu> Joseph O'Rourke,
orourke@sophia.smith.edu writes:
>Message-ID: <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 two-dimensional analog (a square cut into 2 triangles)
and the four-dimensional analog.

Jim King






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