The heart can be expressed in polar coordinates: r =a( 1-sin θ). The area of cardiac line with equation ρ(θ) = a( 1+cosθ) is S = 3 (π a 2)/2. The center line, also called the center line, is a kind of epicycloid and a kind of hub line. It is the trajectory formed when a fixed point on a circle rolls around another circle that is tangent to it and has the same radius. It gets its name because it is shaped like a heart.

The figure of the heart-shaped line between Mandleberg sets is a heart-shaped line. The English name "Cardioid" of the cardiac line was published by de Castillon in the Journal of Philosophy of the Royal Society in 174 1. It means "like a heart".

Extended data

Mathematical expression:

polar equation

Horizontal direction: ρ=a( 1-cosθ) or ρ = a (1+cos θ) (a > 0);

Vertical direction: ρ=a( 1-sinθ) or ρ = a (1+sinθ) (a > 0)。

Cartesian coordinate equation

The expressions of the plane rectangular coordinate system equation of the heart line are x 2+y 2+a * x = a * sqrt (x 2+y 2) and x 2+y 2-a * x = a * sqrt (x 2+y 2) respectively.

parameter equation

x = a *(2 * cos(t)-cos(2 * t))y = a *(2 * sin(t)-sin(2 * t))；

The enclosed area is 3/2 * pi * a 2, and the arc length is 8a.

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