Fig. 621.01 Constant Properties of the Tetrahedron:
- The area of a triangle is one-half the base times
the altitude. Any arbitrary triangle will have the
same area as any other triangle so long as they have
a common base and altitude. Here is shown a
system with two constants, A and B, and two variables_the
edges of the triangle excepting A.
- The volume of a tetrahedron is one-third the base
area times the altitude. Any arbitrary tetrahedron
will have a volume equal to any other tetrahedron so
long as they have common base areas and
common altitudes. Here is shown a system in which there
are three constants, A, B, C, and five
variables_all the tetrahedron edges excluding A.
- As the tetrahedron is pulled out from the cube, the
circumference around the tetrahedron remains
equal when taken at the points where cube and tetrahedron
edges cross; i.e. any rectangular plane
taken through the regular tetrahedron will have a circumference
equal to any other rectangular plane
taken through the same tetrahedron, and this circumference
will be twice the length of the
tetrahedron edge.
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