Park City Mathematics Institute Secondary School Teacher Program Cabri 3D - Steve Phelps

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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