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 Sightseeing Cruises location. In 1962 it bought the famous and venerable Hudson River Day Line, keeping it as a separate brand until 1985. In 1981, the Circle Line split into two companies—Circle Line Sightseeing Cruises and Circle Line Downtown. In 1988 the 42nd Street company bought World Yacht's operating upscale dining cruises from Chelsea Piers - currently World Yacht Dining Cruises. In 1998 the 42nd Street company also launched The Beast, a speedboat ride which takes tourists around the Statue of Liberty and goes 45 mph. In 2007, the United States National Park Service said it was going to terminate Circle Line