#geodesic

[polychroniadis]

Buckminster Fuller’s Montreal geodesic dome on fire, 1976.

[oldshowbiz]

1970s of the Future

[reportsofagrandfuture]

[isomorphismes]

Hadamard knew in 1898 that negative curvature and simply connectedness for surfaces embedded in 3-space force uniqueness of geodesics joining two points—implying that any segment of geodesic is also a shortest path.

But there is a long way toward the modern statement: “on any complete abstract Riemannian manifold of ≥0 curvature of any dimension, curvature is the quotient of its universal covering by a discrete group of isometries.”

Marcel Berger, Riemannian Geometry during the Second Half of the Twentieth Century

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Hadamard, 1898 being Les surfaces à courbure opposées et leurs lignes géodésiques

[mathhombre]

Harriss Geodesics

Edmund Harriss illustrating geodesics on interesting surfaces in wood! From this tweet.

[electronicsquid]

Buckminster Fuller

(Nina Leen. 1944?)

[a-typical]

According to General Relativity, matter warps spacetime, and this warping of spacetime is what we perceive as gravity. Gravitation isn't actually a force, it's a consequence of motion through curved spacetime.

Earths elliptical orbit around the sun is actually a straight line in curved spacetime, this is called a geodesic, a straight line on a curved surface.

So, the sun, for example, curves spacetime (matter telling space how to bend) and objects, like the earth, orbit along that curve (space telling matter how to move).

If matter didn't curve spacetime then nothing would orbit anything and gravity would be nonexistent.

Here's a picture showing a straight line without spacetime curvature and that same line with spacetime curvature.

[mathart]

On drilling holes with minimal redundancy (and with colors!)

The old Mathematica package Graphics`Shapes` featured the function PerforatePolygons[], which drilled a hole in any Polygon[] primitive pres

Most shapes can now be rendered physically via 3D CAD/CAM, but the output of most 3D parametric surface plots is not buildable by 3D printer

Geodesic Hemisphere (Tetrahedral Capillary Unit) by MathArtSPD on Shapeways

Check out Geodesic Hemisphere (Tetrahedral Capillary Unit) by MathArtSPD on Shapeways and discover more 3D printed products in Sculptures.

Tetra Non-Spherical Geodesic Construction Unit by MathArtSPD on Shapeways

Check out Tetra Non-Spherical Geodesic Construction Unit by MathArtSPD on Shapeways and discover more 3D printed products in Sculptures.