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Circle

Plot

Equations

x(t) = a cos(t)
y(t) = a sin(t)

x^2 + y^2 = a^2

r(θ) = a

(for a circle with center at the origin and radius a)

Properties

Basic properties

r = a

d = 2 a

C = 2 π a

A = π a^2

s = 2 π a

d = 2

Conic properties

e = 0

Derived curves

evolute | point at origin
involute | circle involute

Distance properties

mean line segment length | s^_ = (4 a)/π
(where lengths and areas refer to line segments and triangles picked at random from points on the curve)