This is a simulation of the conic section. We can move the plane to cut the conic by using mouse. We add auxiliary line segments to indicate the proof that they are ellipse, parabola, and hyperbola depending on the inclination of the plane.

conic.exe (217KB)

How to use :

shift+m switch for moving the cutting plane

Cutting plane movement switch ON mode:

Left-Drag  Rotation of the cutting plane

Right-Drag  Parallel displacement of the cutting plane

Cutting plane movement switch OFF mode:

Left-Drag  Rotation of the moving direction

Right-Drag  Moving forward and backward

This is a simulation of a model of the universe considered by Kepler, the Platonic Universe. Kepler considered the orbits of the planets are lying over the spheres generated by succesive inclutions of the Platonic Solids. We can explore the Platonic Universe by using mouse.

KeplerUniverse.exe (236KB)

How to use :

Left-Drag  Rotation of the movingdirection

Right-Drag Moving forward and backward

This is a simulation of a light rays from the light source at the focus in the interior of an ellipsoid. It is known that any light rays from the focus must be reflected to path through the other focus. We can move the other focus of the ellipsoid and also the light source by mouse. This is the picture with the light source moved from the focus.

ellipsoid.exe (209KB)

How to use :

shift+f  Switch for moving focus point

Focus moving switch ON mode :

shift+e Switch for moving the right source

Light source moving switch ON mode :

Left-Drag  Move light source

Light source moving switch OFF mode :

Left-Drag  Rotation of the direction from the focus to another one

Right-Drag  Scaling of the distance between the two foci

Focus moving switch OFF mode :

Left-Drag  Rotation of the moving direction

Right-Drag Moving forward and backward