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 ...

Archive for History of Exact Sciences, Vol. 70, No. 1 (January 2016), pp. 1-122 (122 pages) In 1813, J.-V. Poncelet discovered that if there exists a polygon of n-sides, which is inscribed in a given ...

The problem of the in-ancl-circumscribed triangle is a particular case of that of the in-and-circumsrribed polygon; the last-mentioned problem may be thus stated-to find a polygon such that the ...