THE SQUARECIRCLE. The circling of the square.

Here is my original video, “The circling of the square”. I now call the first radial midpoint outline the Squarecircumference.

The content below was added in October 2026.

The second construction, which preserves the enclosed area, is the Squarecircle shown below.

The Squarecircle uses the square root of the average of the squared radial distances. The square, circle and Squarecircle share the same centre and each enclose 10,000 mm².

The Cubisphere: the same volume

This is the Cubisphere construction. It uses the cube root of the average of the cubed radial distances to the concentric cube and sphere. The cube, sphere and Cubisphere each have a volume of 8 cm³. Drag the solid to inspect it, or pause its rotation.

More on shapes and visual ideas

For another work involving circles, see How to draw a vase with snakes and circles + basket ball.

For another design using circular shapes, see Donuts of Jose Romaní’s old crockery.