It takes two things to make a circle.................a point........like a particle...........and a given distance.......the radius.............all the rest of it is measurements..........made from those two things................



Definition

The circumference of a circle is slightly more than three times as long as its diameter. The exact ratio is called π.

π is commonly defined as the ratio of a circle's circumference C to its diameter d:^[8]

${\displaystyle \pi ={\frac {C}{d}}}$

The ratio C/d is constant, regardless of the circle's size. For example, if a circle has twice the diameter of another circle it will also have twice the circumference, preserving the ratio C/d. This definition of π implicitly makes use of flat (Euclidean) geometry; although the notion of a circle can be extended to any curved (non-Euclidean) geometry, these new circles will no longer satisfy the formula π = C/d.^[8] Here, the circumference of a circle is the arc length around the perimeter of the circle, a quantity which can be formally defined independently of geometry using limits, a concept in calculus.^[9] For example, one may compute directly the arc length of the top half of the unit circle given in Cartesian coordinates by x² + y² = 1, as the integral:^[10]