running-executable: Stained Glass




Modern mathematics tends to obliterate history: each new school rewrites the foundations of its subject in its own language, which makes for fine logic but poor pedagogy.
Robin Hartshorne

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The rainbow color map confuses viewers through its lack of perceptual ordering, obscures data through its uncontrolled luminance variation, and actively misleads interpretation through the introduction of non-data-dependent gradients.
David Borland and Russell M. Taylor II, Rainbow Color Map (Still) Considered Harmful




venasaphena: Earliest known neuroscience illustration, depicting the eyes and optic nerves from Ibn al-Haytham’s Kitab al-Manazir (Book of Optics), circa 1027. (x)

venasaphena:

Earliest known neuroscience illustration, depicting the eyes and optic nerves from Ibn al-Haytham’s Kitab al-Manazir (Book of Optics), circa 1027. (x)


hi-res

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Listen to an encoding of someone’s brainwaves whilst sleeping. The frequency was ×70. You can hear that the brainwaves were different during REM sleep 2:30–4:20.

by Anastas Stoyanovsky

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beesandbombs: sphere tangle




Limit set of Maskit’s version of the 11/120 double cusp group. (The colored circle chain reveals the fraction 11/120.) by David J. Wright

Limit set of Maskit’s version of the 11/120 double cusp group. (The colored circle chain reveals the fraction 11/120.)

by David J. Wright

(Source: klein.math.okstate.edu)


hi-res




thegetty:

Cézanne was always looking for the most convincing and honest method of recording his sensation of nature, but ultimately felt himself a failure.

In his later career, he preferred watercolor as a medium for still lives such as this one. He altered both the way we look at the world and the way we record it. 

→ Read more about the beauty and complexity of Cézanne’s watercolors on the Getty Iris here.







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  • Minkowski sum of two shapes
  • direct product of two shapes
  • two complementary planes in 4-D will only intersect at the origin

(polytopes are higher-dimensional polygons … not necessarily regular and they can even go backwards into themselves. Basically a filled-in shape cut out by straight or flat lines/planes/hyperplanes.. So think for example most of the boundary conditions in optimisation. (I usually see something like: a convex function, restricted to a filled-in irregular convex polytope, eg ◣ ⏢ or ◺ ▲ ▶ ◆ , ▷ or ⬠ ⬟ ⌂ 🏠 or a ☖ ☗ ⛊ ⏢ ⬡

(non-polytopes in the Unicode sets where I was searching for those include ◫, ◙, ◶, ▤, ▣, ◐, ◠, ⍟, ⌫, ⌻, ⌘, ⌧, ⌰, ⌑, ⍉, ⍋, ⍾, ⎎, ⎍, ⎌, ⏪, ⏚

You can make a convex polytope from ∩ of half-spaces, or from a convex-hull of vertices.