#geometry

[rauko]

M.C. Escher | METAMORPHOSIS II (1940)

woodcut print in red and black, 19.2cm x 400cm

[blasteffect]

Saturn's north pole !

The hexagon is nearly 30,000 km (20,000 miles) wide. This is large enough that two Earths could fit inside the storm with room to spare.

It is a standing atmospheric wave created by a powerful jet stream that wraps around the pole. Winds along its edges can exceed 300 km/h (about 220 mph).

At the very center of the hexagon lies a deep, dark polar vortex that extends hundreds of kilometers down into Saturn's atmosphere.

Spacecraft/Mission: NASA/JPL-Caltech/SSI (Space Science Institute).

[violetfractal]

A circle inscribed in a square covers 79% of the square.

A ball inscribed in a cube fills 52% of the cube.

A 4-ball inscribed in a hypercube fills 31% of the hypercube.

A 5-ball inscribed in a 5-cube fills 16% of the 5-cube.

⋮

A 9-ball inscribed in a 9-cube fills it up less than 1% of the way, yet there’s no room to fit a second ball of the same size without intersecting the first.

⋮

In dimensions 23 and up, you can fit a little cube in the corner of the diagram, such that the cube has a larger volume than the ball!

That's especially disconcerting because the 23-cube has 8,388,608 corners. Even if you inscribe the little red cubes in all eight million corners, your big cube will still be 99.5% empty space.

[charlesoberonn]

Does Tumblr know about the travesty that is the optimal (as far as we know) configuration to pack 17 squares in a larger square?

[mathani]

A sister to the golden rectangle is a 72-72-36-degree isosceles triangle. Bisecting a base angle reveals a smaller similar triangle.

[d1s4strous]

they're "platonic" solids to YOU. I've had sex with them.

[moodboardmix]

Brutalist Sand Castles by Calvin Seibert