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.

2. 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)

Draw r = Arccos(sinθ) in polar coordinate system, and we will also get a beautiful heart shape. The heart 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.

Extended data

Related stories:

1650, 52-year-old Descartes met 18-year-old Swedish princess Christine on the streets of Stockholm. Descartes, who was down and out at that time, lived a life of begging, and all his possessions were only his tattered clothes and a few math books with him.

On a quiet afternoon, Descartes sat in the street studying math problems as usual. Suddenly, someone came up to him, patted him on the shoulder and turned away. Descartes saw a beautiful young eyelid. She is the little princess of Sweden and the king's favorite daughter Christine.

She bent down, took Descartes' math book and draft paper, and began to talk to him. During the conversation, he found that the little girl was quick-thinking and interested in mathematics. ?

A few days later, he was unexpectedly informed that the king hired him as the little princess's math teacher. Under the guidance of Descartes, Christine walked into the wonderful coordinate world, and every day they were inseparable, they fell in love with each other.

However, it didn't take long for their love affair to reach the king's ears. The king was furious and ordered Descartes to be executed immediately. At Christine's pleading, the king exiled him to China, and the princess was placed under house arrest. ?

At that time, the Black Death was prevalent in continental Europe. Descartes, who was weak, fell ill soon after he returned to France. In the countdown days of life, he wrote to her every day, expecting her reply. However, these letters were intercepted by the king and the princess never heard from him again. ?

Descartes sent Christine his thirteenth letter and died forever. There is not a word written in this last letter, but only one equation: r=a( 1-sinθ).

The king couldn't bear to see his beloved daughter moping every day, so he gave her this letter. Christine, who received the letter, began to draw equation diagrams. A heart-shaped pattern appeared in front of her eyes and she couldn't help crying. This curve is the famous "heart line". ?

Baidu encyclopedia-cardioid line