Park City Mathematics Institute
Secondary School Teacher Program

Cabri 3D - Steve Phelps

 

Where to get Cabri 3D? 
    http://www.chartwellyorke.com/cabri3d/demo.html
    http://www.cabri.com/v2/pages/en/logiciel.php

View Kate Mackrell's An Introduction to Cabri 3D (use the link on her site to download the MS Word version) 

 

Conics - The intersection curve of a double cone and a plane.

Dandelin Spheres - Place two spheres snuggly in a cone. Next, place a plane between the two spheres such that the plane is tangent to the two spheres.  The intersection of the plane and the cone is a conic.  The points of tangency of the planes and the spheres are the foci of the conic.

Desargues Theorem - Two triangles perspective from a point are perspective from a line.

Cube Dissection - a cube can be dissected into three congruent Kammrath pyramids.

Stereographic projection - This is an example of a projection of a sphere onto the plane.  Images of circles on the sphere are circles on the plane.

Another Stereographic projection

A Truncated Cube - Slowly cut off the corners of a cube and observe what happens.

A Truncated Tetrahedron - Slowly cut off the corners and observe what happens

A cube from a tetrahedron

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© 2001 - 2012 Park City Mathematics Institute
IAS/Park City Mathematics Institute is an outreach program of the School of Mathematics
at the Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540

Send questions or comments to: Suzanne Alejandre and Jim King

With program support provided by Math for America

This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.