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    Semicircle

    Plot

    Plot

    Alternate name

    half-circle

    Equations

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

    x^2 + y^2 = a^2 and y>=0

    r(θ) = a

    (for a semicircle lying in the upper half-plane with center at the origin and radius a)

    Properties

    algebraic | closed | convex | parametric | polar | quadratic | semialgebraic | simple

    Basic properties

    A = (π a^2)/2

    s = π a

    d = 2

    Derived curves

    evolute | point at origin

    Distance properties

    mean line segment length | s^_ = (8 (π - 2) a)/π^2 (where lengths and areas refer to line segments and triangles picked at random from points on the curve)

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