Saturday, 1 February 2014

In geometry, Villarceau circles are a pair of circles produced by cutting a torus diagonally through the center at...


In geometry, Villarceau circles are a pair of circles produced by cutting a torus diagonally through the center at the correct angle. Given an arbitrary point on a torus, four circles can be drawn through it. One is in the plane (containing the point) parallel to the equatorial plane of the torus. Another is perpendicular to it. The other two are Villarceau circles. They are named after the French astronomer and mathematician Yvon Villarceau (1813–1883).

Reference:
http://mathworld.wolfram.com/VillarceauCircles.html
Animation by Lucas VB
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5 comments:

  1. tijaj ilea (tijajilea)1 February 2014 at 03:17

    i hed a big problem visualing that cind of things

    ReplyDelete
  2. mimis dog-us1 February 2014 at 04:14

    And all others sections are ellipses. Is it right ?

    ReplyDelete
  3. Hudson Ansley1 February 2014 at 05:09

    Certainly not all ellipses, you can imagine some pretty odd shapes if the plane was just a little off from the example. It would be cool to have an interactive torus -plane intersection to play with...

    ReplyDelete
  4. David Klein1 February 2014 at 07:39

    That symbol is also called vesica pisces.

    ReplyDelete
  5. Adolfo Domínguez17 February 2014 at 15:34

    Interesting, Corina Marinescu

    ReplyDelete

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