Circles and pi · Pulse Beat

For every circle, the circumference divided by the diameter is the same number: π ≈ 3.14159. A small coin and the Earth's equator share it.

For every circle, the circumference divided by the diameter is the same number: π ≈ 3.14159. A small coin and the Earth's equator share it.

So circumference C = π d = 2π r, where r is the radius. The area is A = π r².

Pi is irrational: its decimal digits never end and never repeat, and it cannot be written exactly as a fraction. 22/7 (about 3.1429) and 355/113 (about 3.14159292) are close approximations.

Why r² for area? Cut a circle into thin slices, like a pizza, and lay them alternately point-up and point-down. They form a rough rectangle with height r and width half the circumference, π r. Area = r × π r = π r².

Radians measure angles by arc length: a full turn is 2π radians. They make many formulas in physics and calculus simpler.