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 ...

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 ...

It finds an approximation by determining the length of the perimeter of a polygon inscribed within a circle and the perimeter of a polygon circumscribed outside a circle.