Showing only Notes & Links tagged geometry on art, design, creativity and, technology

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[click here to watch animation]

3D Shadow of a tesseract rotating around a plane in 4D

(via Fourth dimension - Wikipedia, the free encyclopedia)

Cahill-Keyes Megamap prototypes

Fig 7. Another view of the Megamap’s 16-panel assembly prototype, toward a template for the graticule, with a closer view of the Maritime provinces outtake. A single octant would be 62 square meters. The 20 x 40 meter Megamap comprises 800 square meters, but the graticule and geographic contents only occupy 496 of those square-meter panels; the rest are backdrop. The square accent lines now enclose a grid of 200 x 200 mm, where each millimeter represents a kilometer: i.e., a 1/1,000,000 map. These panels were hand-drafted in pencil, using x-y coordinates manually compiled from a Sharp EL-515 calculator, and others output with a BASIC program.

© 1978, 1980, 2009 by Gene Keyes

Photo by Peter Weeks, 1983-10-21

B.J.S. Cahill Introduces Butterfly Map of the World (1909)

B.J.S. Cahill Introduces Butterfly Map of the World (1909)

B.J.S. Cahill Introduces Butterfly Map of the World (1909)

B.J.S. Cahill Introduces Butterfly Map of the World (1909)

B.J.S. Cahill Introduces Butterfly Map of the World (1909)

B.J.S. Cahill Introduces Butterfly Map of the World (1909)

Conical Projection Surface

Dymaxion Projection

This is an animation illustrating Buckminster Fuller’s Dymaxion Map Projection of Earth. While this animation is not mathematically accurate, I think it’s a good illustration of the concept.

Basically, Fuller started with the data for the spherical Earth surface. He projected the data from the sphere onto an icosahedron — the twenty- sided Platonic solid — and then unfolded that icosahedron out flat.

The advantages of this method are many: for one thing, it’s possible to align the surface data with the icosahedron in such a way that, when unfolded, no landmass is cut into, which allows us to see the Earth’s landmasses as one continent (this is where my illustration falls short; note that the landmass is cut into in a couple of spots); also, this method results in nearly no distortion of either size or shape of the landmasses, unlike most other projections (the familiar classroom Mercator map or the Peters projection, for example).