Drawing of stereographic projections of circles on a sphere onto lines in the equatorial plane. Traditional descriptive geometry, axonometry based on the projections from "above" and from "the side". Pencil, watercolor pencil, ballpoint pen, gel pen on watercolor paper.
A line is just a circle, albeit with an infinite radius.
Circles on the surface of the sphere are projected onto the equatorial plane, by connecting each point of the circle to the North Pole and intersecting this connecting ray with the base plane.
The closer a point is to the North Pole, the farther away from the origin of the co-ordinate frame the projection target is. The North Pole itself is mapped onto infinity. In a map of the Earth constructed in this way, the North Pole would be missing; you would need another projection from the South Pole to cover the Northern hemisphere completely.
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…