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
Fife Circle Line line from Inverkeithing that loops back round to Kirkcaldy by an inland route via Cowdenbeath through the old Fife coalfield. Narrowly speaking, just this line could be called the Fife Circle. The current service is actually a combination of two previously separate local routes - Edinburgh to Kirkcaldy & Edinburgh to & . During the 1970s & 80s British Rail only ran a regular daytime service on the Dunfermline line as far as Cowdenbeath; & Cardenden were only served during the weekday business peaks (as can be seen from Table 242 of the UK All Line timetable of that era),