elkemental Force

Art inspired by physics.

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Circles to Circles #4. Stereographic Retrospective.

Circles to Circles #4. Stereographic Retrospective.

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Circles to Circles is a series of six geometric watercolor pencil drawings.

I have revealed number one, two, and three, and this is number four:

Geometric watercolor pencil drawing: Orthographic projection of stereographic projection - a circle on the sphere is projected onto a circle in the equatorial plane. The projection rays form an elliptical cone having its tip at the North Pole. Part of a series of 6six drawings - six differently positioned circles, six different viewpoints. Created and copyright by elkement 2025.
Circles to Circles by elkement 2025.

On this blog, I have probably said anything I had to say about stereographic projection … using words, mathematical symbols, and drawings.

Today, I rather create a retrospective: This is a gallery of all blog posts about stereographic projection, all created before starting the Circles to Circles series.

Digitally enhanced geometrical drawing by elkement 2021-2024. Illustration of the essential steps of a geometrical proof: Why a circle on a sphere is projected stereographically onto a circle in the equatorial plane. Starting point: Both circles are connected by some sort of cone. As the circle on the sphere is not parallel to the base of the cone, it has to be an elliptical one. White lines on black background, selected areas colored by deliberately warped cross-hatching.
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Elliptical Cone. Drawing by elkement 2024. Drawing (mainly watercolor pencils, but all sorts of pens added) using a digital collage of code-generated artworks as a reference (all created by elkement).
Circles to Lines by elkement 2024. Drawing of stereographic projections of circles on a sphere onto lines in the equatorial plane, by elkement 2024. Traditional descriptive geometry, axonometry based on the projections from "above" and from "the side". Pencil, watercolor pencil, ballpoint pen, gel pen on watercolor paper.
Spins and rotations, freehand sketch using the methods of descriptive geometry
Spin Art #1 by elkement 2021. Scientific Visualization / SciArt by elkement 2021. A complex number visualized as a spin, real and imaginary number being the coefficients of a superposition of two orthonormal components, up and down in this case. Showing the alternative perspective by projecting the "spin" stereographically to the equatorial plane, with the coefficients relating in a simple way to the two angles describing the orientation of the spin. The spin "arrow" is inclined by an angle theta with respect to the vertical axis. The projection ray connecting the base of the spin with the South Pole is inclined by half of theta. Created with python / SageMath / threejs.
Elliptical Cone in Stereographic Projection, by elkement 2021. Created with SageMath. A circle on the sphere is projected onto a circle in the equatorial plane.
Elliptical Cone in Stereographic Projection, by elkement 2021. Created with SageMath. A circle on the sphere is projected onto a circle in the equatorial plane.
Geometrical proof by elkement 2021, scan of pencil drawing, lightly colored digitally. Illustration of the essential steps of a geometrical proof: Why a circle on a sphere is projected stereographically onto a circle in the equatorial plane. Starting point: Both circles are connected by some sort of cone. As the circle on the sphere is not parallel to the base of the cone, it has to be an elliptical one.
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elkemental Force
elkemental Force
@elkement.art@elkement.art

Art inspired by physics.

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