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    Circle

    Plot

    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

    algebraic | closed | conic | constant-width | convex | parametric | polar | quadratic | simple

    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)

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