Curved plane solid by fikri arif hakim and the group
Pizza Pie, Unrolled
1. The next slide is a graphic visualization of the fact that Pi ( π ) is always 3.14159… diameters, of any given circle, which is why the circumference, of any circle, equals π r 2 (where r is the radius of the given circle). The cycloid curve—traced by a fixed point on a circle rolling smoothly in a straight line (e.g., a railway wagon wheel)—is close to but not quite circular: it forms an elliptic segment. While the circle is rolled at a fixed speed, the cycloid tracing point moves at varying speeds: at rest, accelerating to the top of the arch, then decelerating back to rest, and so on. Cycloid length = 8 r ( 4 × the defining circle’s diameter (not pi dependent!)), area = 3 π r 2 ( 3 × the defining circle’s area).