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Math Forum » Discussions » Math Topics » geometry.puzzles.independent

Topic: Bisecting A Tetrahedron.
Replies: 6   Last Post: Oct 8, 2010 4:21 PM

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Patrick D. Rockwell

Posts: 52
Registered: 12/12/04
Bisecting A Tetrahedron.
Posted: Aug 25, 2010 7:54 AM
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Let's say that you have a regular tetrahedron whose volume
is 1, and whose altitude is H. Number each face of this tetrahedron
1, 2, 3, and 4.

Then, bisect the tetrahedron with a plane which is parallel to face #1
and
a distance of 0.4H from it. Then bistect it with another plane which
is parallel
to face #2 and again a distance of 0.4H from it, and bistect it with 2
more
planes which are parallel to faces #3 and #4 respectively, and also,
both
a distance of 0.4H from those planes.

What is the volume of the shape that these four planes enclose?

If I'm right, this would also be the probability that if you broke a
stick
into 4 pieces, that the longest piece would be no longer than 0.4 of
the
length of the original stick. Many thanks for any informuation you can
give me.

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