It is obvious that every point on a torus is contained in two circles that lie on the torus. Less obvious is the fact that every such point is contained in two additional circles, called the Villarceau circles.
THINGS TO TRY
Rotate and Zoom in 3D
This code is taken from S. Wagon,
Mathematica in Action
, 3rd ed., forthcoming from Springer-Verlag.
the Wolfram Demonstrations Project
Embed Interactive Demonstration
More details »
Download Demonstration as CDF »
Download Author Code »
More by Author
Orthogonal Systems of Circles on the Sphere
Mark D. Meyerson
Constructing Vector Geometry Solutions
Michael Rogers (Oxford College of Emory University)
Intersection of a Cone and a Sphere
Simple Inequalities in the Unit Cube
Combining Two 3D Rotations
George Beck and Jeff Bryant
Intersecting a Rotating Cone with a Plane
Rotating a Lattice of Points
Exploring Cylindrical Coordinates
Biggest Little Polyhedron
Ed Pegg Jr
Slicing a Sphere along Two Parallel Planes
Browse all topics
Related Curriculum Standards
US Common Core State Standards, Mathematics
The #1 tool for creating Demonstrations
and anything technical.
Explore anything with the first
computational knowledge engine.
The web's most extensive
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
STEM Initiative »
Programs & resources for
educators, schools & students.
Join the initiative for modernizing
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
© 2016 Wolfram Demonstrations Project & Contributors |
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have