Area of a circle "ds" over the whole circle formula_33 is just the arc length, which is its circumference, so this shows that the area "A" enclosed by the circle is equal to formula_34 times the circumference of the circle. Note that the area of a semicircle of radius r can be computed by the integral formula_35. By trigonometric substitution, we substitute formula_36, hence formula_37 The last step follows since the trigonometric identity formula_42 implies that formula_43 and formula_44 have equal integrals over the interval formula_45, using integration by substitution. But on the other hand, since formula_46, the sum of the two integrals is
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