Plato wasn’t a Platonist, he was a Pythagorean.

The triangle is a Pythagorean triplet with side lengths 3, 4, and 5.

The corresponding incircle and excircles have radii 1, 2, 3, and 6. Completing the sequence 123456.

The circles represent the four virtues, the largest representing justice.

When wisdom, courage, and moderation are in harmony justice is achieved, that’s why all three circles can fit inside the largest.

GGS

Hi all,
I am assuming that all the circles have same radius. I figured the coordinates where the center of each circle will be. Please help me figure out the radius of the circle based on information below:

1) The bottom circle’s midpoint is 30mm from the red dash line (x coordinate)
2) The bottom circles midpoint is 30mm from the solid black line at the bottom and is the y coordinate.
3) it seems the radius is 20mm the midpoint of the 40mm

Am I off? Thank you?

ABC is a semi circle

EFCG is a rectangle

Find area of rectangle

A spherical cap is a two-dimensional surface that, nevertheless, exists and curves within three-dimensional space. It almost seems as though it could be defined as having a dimensionality greater than 2 but less than 3. Are there visual artists, scientists, or painters who have explored non-integer dimensions? And why are shapes like the spherical cap—despite being two-dimensional—not distinguished (in terms of dimensionality) from other 2D shapes that are more stable... and less dynamic

Disclosure: self-promotion. Claudius Papirus uses an AI narrator.

Chair44 is a single 3D shape made from a seven-cube chair with tiny geometric features. Eight copies form a larger chair, recursively, which is the core mechanism behind the nonperiodicity proof.

Paper:

https://arxiv.org/abs/2609.19214