Hippopede of Proclus
Hippopede of Proclus |
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Hippopede of Proclus
- Consider a torus, T, as a surface of revolution, generated by a circle with radius r > 0, and with center at distance R > 0 from the axis...
A More Mathematical Explanation
Consider a torus, , as a surface of revolution, generated by a circle [...]
Consider a torus, , as a surface of revolution, generated by a circle with radius , and with center at distance from the axis. is the major radius of , and is the minor radius. Intersecting the torus with a plane parallel to its axis gives a plane curve, called a "spiric section of Perseus." In the special case where this intersecting plane is at distance from the axis, so it is also a tangent plane, the curve is called a "hippopede of Proclus."
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About the Creator of this Image
Adam Coffman is an Associate Professor of Mathematics in the Department of Mathematical Sciences at Indiana University - Purdue University Fort Wayne.
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Hippopede of Proclus |
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Hippopede of Proclus, by Adam Coffman
Found at Adam Coffman --- Lemniscates
Field: Topology
Further Description and Explanation
Consider a torus, , as a surface of revolution, generated by a circle with radius , and with center at distance from the axis. is the major radius of , and is the minor radius. Intersecting the torus with a plane parallel to its axis gives a plane curve, called a "spiric section of Perseus." In the special case where this intersecting plane is at distance from the axis, so it is also a tangent plane, the curve is called a "hippopede of Proclus."
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- The original explaination a very straightforward explaination
- Hippopede from Wikipedia
- Hippopede from Wolfram MathWorld