"Heart-shaped line" is also a common test site in postgraduate mathematics, and its test site mainly involves three equations:

1, polar coordinate 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)。

2, rectangular 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.

3. 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.

Basic attribute

When a= 1, the circumference of the cardiac line is 8 and the closed area is 3π/2.

Heart line is also a kind of line.

The figure in the middle of the Mandelbrot set 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".