Heart line is also a kind of line. The figure between Mandleberg sets is a heart-shaped line. The English name "Cardioid" of the cardiac line was published by de Castillon in the Journal of Philosophy of the Royal Society in 174 1. It means "like a heart".
Cartesian coordinate equation:
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.
Extended data
Story:
It is said that Descartes, a French mathematician, once wandered to Sweden. There, he met Princess Christina of Sweden. A few days later, Descartes received an invitation from the princess, and he became her private math teacher. The princess's math level has advanced by leaps and bounds, and they have been in love for a long time. The princess's father was furious and fired Descartes.
Descartes later wrote many love letters to Princess Christina, but they were all detained by the king. The king opened the letter without his daughter's permission. I thought Descartes would say something, but it turns out that there is only one formula in every letter sent: ρ = a (1-sin θ)? .
During the period after Descartes left, the princess could not eat well or sleep well. The king felt sorry for his daughter, so he took out a letter to her. Anyway, there is nothing written in it, only a mathematical formula.
The princess happily opened every letter and saw the same mathematical formula. Descartes is a great mathematician, and his students are not bad. Love connects them with each other, so she is sure that his formula must contain deeper and more touching feelings than words. Then she draws the formula on the paper. This number is a heart-shaped line.
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