““For our 2D square, this diagonal length is sqrt 2 = 1.414; ....The diagonal from the centre of each padding sphere to the centre of the cube is sqrt 3 = 1.732, which allows our specimen sphere to expand to a radius of .732:.....The distance from the centre of each padding 4-sphere to the centre of the 4D box is a very exact and tidy 2 (i.e. sqrt4), givimg our centre specimen sphere a radius of 1....Onwards to 5 dimensions and things start to get a bit strange: our specimen sphere has continued growing and now has a radius of 1.236, bigger than the padding spheres around it.....The big surprise is when the box enters ten dimensions and the inner sphere's radius hits 2.162, which means that it is actually reaching outside the box....From twenty-six dimensions onwards, the sphere is more than twice as big as the box it's inside.””
