A digitally enhanced mathematical proof originally drawn on paper: Why circles are projected onto circles stereographically.
The circle on the sphere and its image in the equatorial plane are both connected by some sort of cone. If the circle would be the base of the cone, the intersection with a plane would be an ellipse. As the intersection is a circle, the base must be an ellipse. I am looking at this cone, from a direction perpendicular to the cone's axis. The actual proof that circles are projected onto circles is carried out by spotting various triangles and angles in this sketch.
I have drawn it in 2021 when I was not yet sure if it should be just a proof or also art. In 2024 I have been sure it should be both! I want to prove (:-)) that also "sparse mathematics" can be beautiful.
Created on paper, scanned and inverted, digital overlay created with Procreate. No AI!
Elke Stangl (elkement) (she/her) is an Austrian physics PhD working as an engineer. Her mathematical art is borne out of her life-long passion for the theoretical underpinnings of her craft. She is creating virtual three-dimensional structures from mathematical functions – digitally with code or with ruler and compass, using.. Read more…