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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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