In brief. In the window below, the Mathematicians torus rotates freely in four dimensional space before being projected onto three dimensional space.
In detail. By dragging your mouse over the torus, you can rotate the projection of the torus in three dimensions, as it is simultaneously rotating in four dimensions.
By clicking on the rotation on/off button, you can pause the four-dimensional rotation. You will still be able to rotate the projected torus in three dimensions.
The wire/solid/ribbon frame button toggles between a wire frame representation of the Mathematicians torus, a solid representation, and a sliced representation.
The slider on the bottom of the window controls the size of the radii of the two circles that form the Mathematicians torus. When the slider is in the center, the circles have the same radius: as in our definition of the Mathematicians torus. However, we can extend our definition so that the Mathematicians torus is the Cartesian product of two circles with different radii. Moving the slider to the left or right will decrease the radius of one of the circles, while leaving the other radius fixed.
Copyright © 2016 by Jason Hanson and DigiPen Institute of Technology