Volume of the tetrahedron
Taking two diagonals of two opposite sides of a cube and attaching them properly we get a tetrahedron.
This can be generalized to any parallelepiped and we get not regular "tetrahedra" .
In the applet we show that the volume of the tetrahedron is one third of the cube (or parallelepiped) that contains it.
Therefore, the volume of a regular tetrahedron is
The vertical cursor allows us to slicing away some parts of the cube and we can see the tetrahedron inside.
If we click and drag on the figure we can rotate it.
REFERENCES
Howard Eves, mathematician and historian of Mathematics, received the George Polya Award
for the article Two Surprising Theorems on Cavalieri
Congruence.
LINKS
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Sections in Howard Eves's tetrahedron
Howard Eves, mathematician and historian of Mathematics, received the George Polya Award for the article Two Surprising Theorems on Cavalieri Congruence
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Sections in the sphere
We want to study a surprising Cavalieri congruence between a sphere and a tetrahedron. In this page we can see sections in a sphere.
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Surprising Cavalieri congruence between a sphere and a tetrahedronn
We show a sphere and the Howard Eves's tetrahedron with congruent sections.
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Volume of an octahedron
The volume of an octahedron is four times the volume of a tetrahedron.
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