Area of a circle each polygon side is a radius, of length "r". And since the total side length is greater than the circumference, the polygon consists of "n" identical triangles with total area greater than "T". Again we have a contradiction, so our supposition that "C" might be less than "T" must be wrong as well. Therefore, it must be the case that the area enclosed by the circle is precisely the same as the area of the triangle. This concludes the proof. Following Satō Moshun and Leonardo da Vinci , we can use inscribed regular polygons in a different way. Suppose we
Outer Circle railway line Outer Circle railway line The Outer Circle was built in 1891 as a steam-era suburban railway line, in Melbourne, Australia. It covered much of the modern City of Boroondara, including the suburbs of (from north to south) Kew East, Camberwell, Burwood, Ashburton, and Malvern East. At its longest stage, it ran from Fairfield station, on what is today the Hurstbridge line, to Oakleigh station, on the current Pakenham and Cranbourne lines. The Outer Circle railway was first advocated by a group known as the Upper Yarra Railway League in 1867 who suggested that the Gippsland Railway could be brought into