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Bisecting A Tetrahedron.
Posted:
Aug 25, 2010 7:54 AM


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.



