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
Line Describing a Cone allowed him to actualize his ideas on the relationship between viewer and film and the medium of film itself. The thirty-minute film begins with a single white dot projected onto a black surface. As time progresses, the dot begins to form a curved line, tracing the circumference of a circle until the end of the line reaches its starting point. Meanwhile, particles in the air reveal the path of light in the space between the projector and the wall, making visible a cone of light. If the artist's display specifications are met, this beam of light projects between thirty and