Surprising Cavalieri congruence between a sphere and a tetrahedron
We have seen that the areas of the sections in one sphere are:
The corresponding areas of the sections in the Howard Eves's tetrahedron are equal
Therefore, Howard Eves claims that
"Theorem 2. There exist a tetrahedrom to witch a give sphere is Cavalieri congruent."
The vertical cursor allows us to change the height of the section.
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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Cavalieri: The volume of a sphere
Using Cavalieri's Principle we can calculate the volume of a sphere.
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Kepler: The volume of a wine barrel
Kepler was one mathematician who contributed to the origin of integral calculus. He used infinitesimal techniques for calculating areas and volumes.
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