Area of a circle inscribe a hexagon. Cut the hexagon into six triangles by splitting it from the center. Two opposite triangles both touch two common diameters; slide them along one so the radial edges are adjacent. They now form a parallelogram, with the hexagon sides making two opposite edges, one of which is the base, "s". Two radial edges form slanted sides, and the height, "h" is equal to its apothem (as in the Archimedes proof). In fact, we can assemble all the triangles into one big parallelogram by putting successive pairs next to each other. The same is true if we increase
Angles between flats Angles between flats The concept of angles between lines in the plane and between pairs of two lines, two planes or a line and a plane in space can be generalized to arbitrary dimension. This generalization was first discussed by Jordan. For any pair of flats in a Euclidean space of arbitrary dimension one can define a set of mutual angles which are invariant under isometric transformation of the Euclidean space. If the flats do not intersect, their shortest distance is one more invariant. These angles are called canonical or principal. The concept of angles can be generalized to pairs