Elementary Geometry
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.
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.
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.
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
"If we do not succeed in solving a mathematical problem, the reason frequently consists in our failure to recognize the more general standpoint from which the problem before us appears only as a single link in a chain of related problems."
The new web page of the laboratory was uploaded.
You may feel free to click and download the executable files to experience the virtual mathematical world..
These programs work for Windows platform and require the dll file "glut32.dll" in the System32 folder.
If you have any questions, simply mail me at