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
Circle line (London Underground) the southern portion of the line. Due to conflict between the two companies it was not until October 1884 that the inner circle was completed. The line was electrified in 1905, and in 1933 the companies were amalgamated into the London Passenger Transport Board. In 1949 the Circle line appeared as a separate line for the first time on the Tube map. In 2009 the closed loop around the centre of London on the north side of the River Thames was broken at Edgware Road and extended west to become a spiral to Hammersmith. The signalling system is being upgraded