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
Outer Circle railway line Belgrave and Lilydale lines) with Oakleigh station to the south, via Riversdale on what is now the Alamein line. The final section was north from Riversdale through to Fairfield station (then called Fairfield Park station). There was also a branch line from the closed Waverley Road station (near the modern East Malvern station) to Darling and Burnley. This was the first section of what is now the Glen Waverley line and was opened a few weeks before the Outer Circle. When opened the line was in length, and had 11 stations, all provided with twin platforms and crossing loops. Provision