Area of a circle Archimedes is not rigorous by modern standards, because it assumes that we can compare the length of arc of a circle to the length of a secant and a tangent line, and similar statements about the area, as geometrically evident. The area of a regular polygon is half its perimeter times the apothem. As the number of sides of the regular polygon increases, the polygon tends to a circle, and the apothem tends to the radius. This suggests that the area of a disk is half the circumference of its bounding circle times the radius. Following Archimedes' argument in "The
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),