Difference between revisions of "Hippopede of Proclus"
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+ | {{Image Description | ||
+ | |ImageName=Hippopede of Proclus | ||
+ | |ImageURL=http://www.ipfw.edu/math/Coffman/images/proc.gif | ||
+ | |Image=HippopedeofProc.gif | ||
+ | |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... | ||
+ | |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." | ||
+ | |AuthorName=Adam Coffman | ||
+ | |AuthorDesc=Adam Coffman is an Associate Professor of Mathematics in the Department of Mathematical Sciences at Indiana University - Purdue University Fort Wayne. | ||
+ | |SiteName=http://www.ipfw.edu/math/Coffman/images/proc.gif | ||
+ | |SiteURL=Adam Coffman --- Lemniscates | ||
+ | |Field=Topology | ||
+ | |FieldLinks=:*[http://en.wikipedia.org/wiki/Hippopede Hippopede from Wikipedia] | ||
+ | :*[http://mathworld.wolfram.com/Hippopede.html Hippopede from Wolfram MathWorld] | ||
+ | |AuthorLinks=:*http://www.ipfw.edu/math/Coffman | ||
+ | |Pre-K=No | ||
+ | |Elementary=No | ||
+ | |MiddleSchool=No | ||
+ | |HighSchool=No | ||
+ | |HigherEd=Yes | ||
+ | |InformalEd=No | ||
+ | }} | ||
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Revision as of 22:42, 2 July 2008
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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[[image:|center]] |
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."
About the Author
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Related Links
Additional Topology Resources
Other Materials By Adam Coffman
- The original explaination a very straightforward explaination
- Hippopede from Wikipedia
- Hippopede from Wolfram MathWorld