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Wednesday, June 18, 2025

Plato’s “Divided Line” via Euclid’s Similar Triangles

Filed under: General — Tags: Art Space, Cover Art, Lines — m759 @ 9:41 am

The above figure conceals three "divided lines," each
divided in the same proportion. These three bent divided lines
AHB, BHC, and ABC are each bent at a division point into two
line segments joined at a right angle.

_AH _{BH AB}
^__ ₌^__₌^__ .
^{HB HC BC}

Tuesday, June 17, 2025

A title from 1959 —

Filed under: General — Tags: Cover Art, Sleepwalkers, Warmed Over — m759 @ 8:02 pm

See a New York Times review from May 24, 1959.

For musical accompaniment from later that year,
see the previous post.

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Lines

Filed under: General — Tags: Art Space, Cover Art, Lines — m759 @ 5:40 am

Related geometry . . .

"Drop me a line" — Request attributed to Emma Stone.

Meditation on the dropped line —

Analogous "dividing line" . . .

The Klein quadric, PG(5,2), and the 'bricks' of the Miracle Octad Generator

Related vocabulary: Stoicheia.

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