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nextstep
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Joined: 06 Jan 2007
Posts: 539
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 Posted: Sat Nov 15, 2014 4:51 am Post subject: Duplin Cyclide |
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Hi,
a Dupin cyclide or cyclide of Dupin is any geometric inversion of a standard torus, cylinder or double cone. In particular, these latter are themselves examples of Dupin cyclides. They were discovered by Charles Dupin in his 1803 dissertation under Gaspard Monge.The key property of a Dupin cyclide is that it is a channel surface (envelope of a one parameter family of spheres) in two different ways. This property means that Dupin cyclides are natural objects in Lie sphere geometry.
 DuplinCyclide by taha_ab, on Flickr
| Quote: | {
"Iso3D": {
"Name": [
"DuplinCyclides"
],
"Component": [
"DuplinCyclides"
],
"Fxyz": [
"(2^2 - (2 + 2.1)^2) * (2^2 - (2 - 2.1)^2)*(x^4+y^4+z^4)+ 2*((2^2 - (2 + 2.1)^2 )*(2^2 - .1^2)* (x^2 * y^2+x^2 * z^2+y^2 * z^2))+2* 2^2 *((2.1^2)* (2 *x *2-2^2))*(x^2+y^2+z^2)+ 4 * 2^4 * (2 *x)* (-2^2+2 * x)+4* 2^4 * 2.1^2 * y^2+2^8"
],
"Xmax": [
" 2.2"
],
"Xmin": [
"-2"
],
"Ymax": [
" 2.1"
],
"Ymin": [
"-2.1"
],
"Zmax": [
" 1.3"
],
"Zmin": [
"-1.3"
]
}
} |
More at :
https://www.facebook.com/pages/MathMod/529510253833102
http://en.wikipedia.org/wiki/Dupin_cyclide
_________________
Cheers,
Abderrahman |
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nextstep
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