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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The volume of the tetrahedron
The volume of a tetrahedron is one third of the prism that contains it.
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Sections on a tetrahedron
Special sections of a tetrahedron are rectangles (and even squares)
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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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Cavalieri: The volume of a sphere
Using Cavalieri's Principle we can calculate the volume of a sphere.
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Sections in the sphere
We want to calculate the surface area of sections of a sphere using the Pythagorean Theorem. We also study the relation with the Geometric Mean and the Right Triangle Altitude Theorem.
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