Sections in Howard Eves's tetrahedron
Howard Eves describes a tetrahedron as follows:
... draw two line segments AB and CD perpendicular to one another, each of length
and having the line segment joinning their midpoints as a common perpendicular. "
The distance between these two lines is 2r.
This tetrahedron can be considered within a prism of a square base and height 2r.
The side of the square is
Therefore, the volume of the tetrahedron is
If x is the distance from the plane of the section that represents the applet to the center of the tetrahedron, the area of the section is
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 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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