Sections on a tetrahedron
We have already seen that the volume of a tetrahedron (in general, not regular) we can obtain joining the diagonals of the faces of a parallelepiped is a third the volume of that parallelepiped.
In this applet we can see the sections of a tetrahedron built from a parallelepiped square base.
In the initial position, the applet displays a regular tetrahedron cut in half by a square section. It is a well-known puzzle formed by these two pieces alike.
It is easy to calculate the area of those sections. It's what we do in a particular case on the page devoted to the sections of Howard Eves's tetrahedron.
The cursors control the height of the section, the size of the edges of the bases of the prism and the separation between the two pieces.
If we click and drag on the figure we can rotate it.
REFERENCES
LINKS
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The volume of the tetrahedron
The volume of a tetrahedron is one third of the prism that contains it.
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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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