[nplobrmf] Square in circle

Draw a square with half the area of a circle with radius 1.  If placed concentric, the corner will be 0.8862269254527578 from the center.  The square fits entirely in the circle, so the area outside the square equals the area of the square.

In 3 dimensions, the corner will "stick out".  Half the space diagonal is 1.1080265568948648.

In 4 dimensions, the corner sticks out even more: 1.2533141373155001 . The distance from center to corner in a 4D hypercube (tesseract) is the same as the length of an edge; one can have a weird overlapping pattern of diagonal and orthogonal cubes. It's also like a 2D hexagon, and the hexagonal flower pattern one can easily draw with a compass.

Compare with circle in square