A heart-shaped line is a trajectory formed when a fixed point on a circle rolls around another circle that is tangent to it and has the same radius. It is named because it looks like a heart.
The function of r = a (1-sinθ) has two variables, which can be assigned to a and solved.
The function image is a heart-shaped line. This equation is also called "Cartesian love coordinate formula".
As shown in the figure, the images are a= 1, a=2 and a=3 respectively.
Extended data:
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 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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