Difference between revisions of "Hippopede of Proclus"

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{{Image Description 2|imgnm=Hippopede of Proclus|author=Adam Coffman|surl=http://www.ipfw.edu/math/Coffman/pov/spiric.html|sname=Adam Coffman --- Lemniscates|iurl=http://www.ipfw.edu/math/Coffman/images/proc.gif|field=Topology|adesc=an Associate Professor of Mathematics in the Department of Mathematical Sciences at Indiana University - Purdue University Fort Wayne.|desc=
 
Consider a torus, <math>T</math>, as a surface of revolution, generated by a circle with radius <math>r > 0</math>, and with center at distance <math>R > 0</math> from the axis. <math>R</math> is the ''major radius'' of <math>T</math>, and <math>r</math> is the ''minor radius''. Intersecting the torus <math>T</math> 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 <math>|R - r|</math> from the axis, so it is also a tangent plane, the curve is called a "hippopede of Proclus."
 
 
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*[http://www.ipfw.edu/math/Coffman/pov/spiric.html The original explaination] a very straightforward explaination
 
*[http://en.wikipedia.org/wiki/Hippopede Hippopede from Wikipedia]
 
*[http://mathworld.wolfram.com/Hippopede.html Hippopede from Wolfram MathWorld]
 

Revision as of 22:44, 2 July 2008


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

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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