Vertical direction: p=a( 1-sinθ) or p = a (1+sinθ) (a > 0)。

According to legend, Descartes' formula of heart line is the content of the thirteenth letter that Descartes, a famous French mathematician, wrote to his lover Princess Christine. This is the only mathematical formula in this letter. Draw the whole curve of this formula, which is the famous heart line!

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.

Descartes sent Christine his thirteenth letter and died forever. At this time, the little princess under house arrest is still wandering in the corridor of the palace, thinking of her lover in the distance. There is not a word written in this last letter, but only one equation: r=a( 1-sinθ).

The origin of Descartes' heart;

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. Descartes, with a lofty nature, never asked passers-by for alms. He just silently bowed his head and wrote on the paper, focusing on his mathematical world.

On a quiet afternoon, Descartes sat in the street as usual, bathed in the sun and studied math problems. Suddenly, someone came up to him and patted him on the shoulder. "What are you doing?" Turning around, Descartes saw a beautiful young face, a pair of clear eyes like a blue lake, very cute, with long eyelashes blinking. 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. Confused Descartes came to the palace with the guards who came to inform him. While waiting in the living room, he heard a silvery laughter coming from a distance. Turning around, he saw the girl he met in the street a few days ago. In desperation, he bowed his head and saluted.

From then on, he took advantage of the princess's math teacher.

Under the careful guidance of Descartes, the princess's mathematics advanced by leaps and bounds, and they began to become close. Descartes introduced her to his new research field-rectangular coordinate system. Through it, algebra and geometry can be combined, which is the embryonic form of analytic geometry founded by Descartes later. Under the guidance of Descartes, Christine entered the wonderful coordinate world, and she was fascinated by curves. Being inseparable every day also makes them fall in love.