#stereographicprojection — Public Fediverse posts

Circles to Lines (2026)

Circles and lines - that sounded manageable. So, this was one of my first attempts at reviving descriptive geometry. A circle on a sphere is projected into a circle in the equatorial plane under stereographic projection. But if the source circle contains the North Pole, the projection ray in this point becomes tangent to the sphere and parallel to the equatorial plane. Thus circles containing the North Pole are projected into lines - circles with infinite radii. The drawing shows this […]

https://elkement.art/2026/04/10/circles-to-lines-2026/

Circles to Circles #3. Using the Invisible Simple Box

When you do your geometry homework, everything fits nicely on a sheet of standard paper. Problems have been carefully designed to make this happen! I had never appreciated this - until I created my own geometry challenges. Either the different views were overlapping too much or interesting features were pushed beyond the edges of the paper. Lines were intersecting at such shallow angles that the intersection points could not be determined exactly. To make at least the orthographic view more […]

https://elkement.art/2025/05/25/circles-to-circles-3-using-the-invisible-simple-box/

Circles to Circles #2. A Friendly Death Star.

My art should speak for itself, as an abstract geometric drawing. But if you are so inclined, you can decode the math. Mathematics shows up twice: In the thing I am depicting, and in the techniques I am using to draw it geometrically. The series Circles of Circles is about stereographic projection of circles onto circles, and I am using orthographic projection as a tool. In a sense this is "orthographic projection of stereographic projection" Circles to Circles #2 by elkement 2025, […]

https://elkement.art/2025/05/22/circles-to-circles-2-a-friendly-death-star/

Circles to Circles #1. On Descriptive Geometry.

I am not a hoarder. I parted with school memorabilia long ago. When I started reading books on e-readers, the remaining books felt like an odd time capsule. They were not representing my reading self anymore. So, I got rid of most books, too. There was one exception: I still have my high school Descriptive Geometry books. "DG" was taught for the two last years of high school, in grade 7 and 8 (age 17 - 18). I remember it as pure delight - learning how to depict three-dimensional objects […]

https://elkement.art/2025/05/16/circles-to-circles-1-on-descriptive-geometry/