# Difference between revisions of "Hippopede of Proclus"

Hippopede of Proclus
Field: Topology
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."

# 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.