Proven Cone (2025) Drawing by Elkement (Elke Stangl)

Not For Sale

Seller Elkement (Elke Stangl)

Fine art paper, 8x11 in
  • Original Artwork (One Of A Kind) Drawing, Pencil / Digital Painting on Paper
  • Dimensions Dimensions are available on request
  • Artwork's condition The artwork is in perfect condition
  • Framing This artwork is not framed
  • Categories Geometric Science
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 [...]
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!

Related themes

Science Mathematics Proof Drawing Circles

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elkement is crafting virtual sculptures with code (no AI!) and with pencils - structures based on mathematical functions. Her art is based on and inspired by physics, engineering, and tech. Inspired by the aesthetics [...]

elkement is crafting virtual sculptures with code (no AI!) and with pencils - structures based on mathematical functions. Her art is based on and inspired by physics, engineering, and tech. Inspired by the aesthetics of vintage patent drawings and by Sir Roger Penrose’s handcrafted sketches, elkement is searching for the nexus of science and art.

elkement enjoys spotting the uncanny in the allegedly simple and mundane. Having created virtual three-dimensional structures with code, she is always searching for an unusual perspective to challenge preconceived notions. She often juxtaposes her visual art with her Found Poetry when she presents her art (at elkement.art).

Recurring motifs in elkement's digital art are diffraction patterns. Since early childhood, elkement had been fascinated by the pure spectral colors of the rainbow and by the physics underlying their creation. Forming structures from diffraction patterns that are both based on exact math and that resemble the patterns you actually see encapsulates the beauty of the phenomena as everybody can experience them, as well as the beauty of the underlying math. 

elkement is a physicist by training who fondly remembers her high school classes in descriptive geometry and fine art.

(In case you read this in a language other than English, it is an automated translation.)

This gallery profile was in March 2022. Profits for artworks created in 2022 go to Ukraine aid - to 'Cards for Ukraine' - a small, transparent organization helping Ukrainian refugees in Austria. 

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