Difference between revisions of "Hippopede of Proclus"

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{{Image Description
 
{{Image Description
 
|ImageName=Hippopede of Proclus
 
|ImageName=Hippopede of Proclus
|ImageURL=http://www.ipfw.edu/math/Coffman/images/proc.gif
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|Image=HippopedeOfProc.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...
 
|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."
+
|Pre-K=No
 +
|Elementary=No
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|MiddleSchool=No
 +
|HighSchool=No
 +
|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."
 
|AuthorName=Adam Coffman
 
|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.
 
|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
+
|SiteName=Adam Coffman --- Lemniscates
|SiteURL=Adam Coffman --- Lemniscates
+
|SiteURL=http://www.ipfw.edu/math/Coffman/images/proc.gif
 
|Field=Topology
 
|Field=Topology
 
|FieldLinks=:*[http://en.wikipedia.org/wiki/Hippopede Hippopede from Wikipedia]
 
|FieldLinks=:*[http://en.wikipedia.org/wiki/Hippopede Hippopede from Wikipedia]
 
:*[http://mathworld.wolfram.com/Hippopede.html Hippopede from Wolfram MathWorld]
 
:*[http://mathworld.wolfram.com/Hippopede.html Hippopede from Wolfram MathWorld]
 
|AuthorLinks=:*http://www.ipfw.edu/math/Coffman
 
|AuthorLinks=:*http://www.ipfw.edu/math/Coffman
|Pre-K=No
+
|InProgress=Yes
|Elementary=No
 
|MiddleSchool=No
 
|HighSchool=No
 
|HigherEd=Yes
 
|InformalEd=No
 
}}
 
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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."
 
 
 
 
}}
 
}}
*[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]
 

Latest revision as of 09:20, 10 June 2011

Inprogress.png
Hippopede of Proclus
HippopedeOfProc.gif
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."




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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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