Difference between revisions of "Hippopede of Proclus"

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|ImageName=Hippopede of Proclus
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|ImageURL=http://www.ipfw.edu/math/Coffman/images/proc.gif
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|Image=HippopedeofProc.gif
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|ImageIntro=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...
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|ImageDesc=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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|AuthorName=Adam Coffman
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|AuthorDesc=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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|SiteName=http://www.ipfw.edu/math/Coffman/images/proc.gif
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|SiteURL=Adam Coffman --- Lemniscates
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|Field=Topology
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|FieldLinks=:*[http://en.wikipedia.org/wiki/Hippopede Hippopede from Wikipedia]
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:*[http://mathworld.wolfram.com/Hippopede.html Hippopede from Wolfram MathWorld]
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Revision as of 22:42, 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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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."

About the Author

Category:Adam Coffman

Other Topology Images

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Related Links

Additional Topology Resources

Other Materials By Adam Coffman