Archimedes determined the upper and lower range of pi by finding the perimeters of inscribed and circumscribed polygons. By doubling the number of sides of the hexagon to a 12-sided polygon, then ...

A plane polygon P inscribed in a conic C and circumscribed to a conic D can be continuously 'rotated', as it were. One of the many proofs consists in viewing each side of P as translation by a torsion ...

In this paper we prove asymptotic upper bounds on the variance of the number of vertices and the missed area of inscribed random disc-polygons in smooth convex discs whose boundary is $C_ + ^2$.

“THE first four books of Euclid: or the principal properties of triangles, and of squares and other parallelograms treated geometrically: the principal properties of the circle and its inscribed ...