Bianca Violet and Valentina Galata

IMAGINARY project manager
Mathematisches Forschungsinstitut Oberwolfach
Berlin, Germany

I enjoy visualizing simple geometric beauty combined with mathematical content.

Algebraic Apple
Algebraic Apple
60 x 60 cm
digital image (will be printed)

Take a doughnut shaped ring torus and increase the radius of the tube until the inner hole just disappears. You arrive at a singularity in the middle of the object, where the two cusps meet. To increase the resemblance to an ordinary apple, stretch the whole surface a little along the rotational axis and add a stem.

Each point in space can be described by three coordinates x, y and z. All of the points within the apple skin satisfy the following algebraic equation:
x² + y² - (x² + y² + z²/2)² = 0

The apple is cut by showing only points that lie on one side of a chosen cutting surface, which can be a plane, a sphere, or something else. All points on the other side of the surface are simply cut off (or eaten).