x(t)=a(2cost-cos2t)
y(t)=a(2sint-sin2t)
The general equation is x? +y？ +ax=a*sqrt(x？ +y？ ) and x? +y？ -ax=a*sqrt(x？ +y？ )
The equation in the polar coordinate system is:
ρ(θ)=2r( 1+/-cosθ)
P(θ)=2r( 1+/-sinθ)
Where r is the radius of the circle. The cusp of the curve is located at (r, 0)
Extended data:
-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.
Solution of closed area: Take ρ=a( 1+cosθ) as an example.
Let the area element be dA, then
dA = 1/2 * a∧2 *( 1+cosθ)∧2 * dθ
The area of the upper half shaft is obtained by integral method.
a =∫(π→0) 1/2 * a∧2 *( 1+cosθ)∧2 * dθ
=3/4*a∧2*π
So the area enclosed by the whole heart line is S=2A=3/2*a∧2*π.
Alternatives:
1, draw r = Arccos(sinθ) in polar coordinates, and we will also get a beautiful heart line.
2. More complicated heart lines.
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.
References:
Baidu encyclopedia-heart line