circonférence

Circumference is the length of a circle’s boundary. In French, the term for this concept is circonférence. In geometry, it represents the distance around the circle and is a fundamental measure alongside area and radius.

The circumference C can be computed from either the radius r or the diameter d. The standard formulas are C = 2πr and C = πd, where π (pi) is the constant equal to the ratio of a circle’s circumference to its diameter. Pi is approximately 3.14159 and is the same constant across all circles.

The circumference is a linear measure, with units matching those used for length, such as meters, centimeters, or inches. By comparison, the area of a circle is A = πr^2, which grows with the square of the radius, illustrating how circumference and area relate differently to size.

For a general arc, the length s subtended by a central angle θ (in radians) is s = rθ. When θ equals 2π, the arc becomes the full circle, yielding C = 2πr. This links the curved length of parts of a circle to the whole circumference.

Applications of the circumference include sizing wheels, pipes, belts, circular fences, and any measurement involving round objects. The concept has a long mathematical history, with pi being approximated by ancient civilizations and refined by later mathematicians such as Archimedes, who used inscribed and circumscribed polygons to bound its value.