# Difference between revisions of "Hippopede of Proclus"

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Hippopede of Proclus
Field: Topology
Image Created By: Adam Coffman
Website: [Adam Coffman --- Lemniscates ]

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, $T$, as a surface of revolution, generated by a circle [...]

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. $R$ is the major radius of $T$, and $r$ is the minor radius. Intersecting the torus $T$ 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 $|R - r|$ 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
[[image:|center]]
Field: Topology
Author: Adam Coffman
Website: Adam Coffman --- Lemniscates

Hippopede of Proclus, by Adam Coffman
Found at Adam Coffman --- Lemniscates
Field: Topology

## Further Description and Explanation

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. $R$ is the major radius of $T$, and $r$ is the minor radius. Intersecting the torus $T$ 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 $|R - r|$ from the axis, so it is also a tangent plane, the curve is called a "hippopede of Proclus."

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