According to the following polar coordinate equation, and then bring in different parameters, you can get a heart drawn by the heart line.

ρ=a( 1+cosθ) (heart type facing right)

ρ=a( 1-cosθ) (heart type facing left)

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.

Parametric equation:

-pi & lt； = t & lt=pi or 0

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. Draw a graph:

Extended data:

Alternative heart-shaped line drawing:

1, draw r = Arccos(sinθ) in polar coordinates, and we will also get a beautiful heart line.

2. More complex heart-shaped patterns:

3. The heart-shaped line in the plane rectangular coordinate system created by math enthusiasts consists of two function expressions, but when drawing with the geometric sketchpad, please be sure to change the angle unit from the default degree to radian.