"What is it?", Natalie curiously opened the box and took out a silver bracelet with a small squirrel hanging from it, in addition to a string of mathematical symbols.

"Why a squirrel?", she was a little puzzled, pinching the bracelet between her eyes, and casting an inquiring look at Lu Qiujian, "And what does this string of symbols mean?"

"This kind of thing has to be guessed by yourself to be interesting!", Lu Qiujian shook his hand to indicate that he would not tell her the answer directly, "But I can give you a hint, what do squirrels like to eat the most?"

"Nut!" (Nut, pronounced very similar to Natalie's nickname Nat), Natalie reflected in an instant, "Oh, Lui, you bad guy!", the squirrel likes Nut, and her name is Nat, so the meaning of this bracelet is clear.

"Bingo!, you guessed it!", Lu Qiujian snapped his fingers in celebration, looked down at Natalie's eyes, and saw a trace of shyness and tenderness in her eyes, not to mention the heartbeat after being hit in the softest part of his heart;

"Well, it seems to be a mathematical formula?r=a(1-sinθ)?", Natalie is also a top student at Harvard, although she studied psychology, she is no stranger to mathematics, and she quickly saw the origin of this string of symbols, but what is this formula? Since the squirrel is a sign of liking Nat, then this string of formulas also has a special meaning, right?

"Exactly!", Lu Qiujian applauded, and asked the waiter to borrow a pen and paper and hand it to Natalie, "In addition to using formulas, equations can also be used as graphs to express, you can draw this formula on polar coordinates and look at it!"

Polar coordinates are the same as Cartesian coordinates, they are all reference systems introduced to represent the position of the point in space, Cartesian coordinates are used to determine the coordinates by using the distance and position relationship between the point and each coordinate axis, and polar coordinates are used to represent points with angles and distances, it will be simpler to use polar coordinates when dealing with some problems, for example, in Cartesian coordinates, the standard equation of the circle centered at the origin is x^2+y^2=R^2, where R is the radius, and the same circle, the equation in the polar coordinates can be written as ρ=R, thus greatly simplifying the equation.

This math was not difficult for Natalie, who quickly picked up a pen and sketched a coordinate system on the paper, then marked the numbers on the coordinate system and began to make a diagram.

At the intersection of two straight lines, an arc extending to the upper left is crossed, the arc crosses a small arc and continues to expand outward after crossing the abscissa line, and then retracts inward until it reaches the vertical coordinate line;

"Wow!", a beautiful heart appeared on the coordinate system, and Natalie let out a heartfelt admiration, "This equation is so beautiful!

"There's a romantic story here!", Lu Qiujian began to tell in a deep voice, "In 1649, on the streets of Stockholm, 52-year-old Descartes met 18-year-old Swedish princess Christine. A few days later, he was unexpectedly informed that the king had hired him as the little princess's math teacher. Following the guards who came to inform him to the palace, he met a girl he met on the street. From then on, he became the little princess's math teacher. ”

"And then?", Natalie asked as eagerly as an ordinary little girl.

Sure enough, every girl has a princess dream in her heart, even Natalie is not exempt from vulgarity, Lu Qiujian continued, "The little princess's mathematics has advanced by leaps and bounds under the careful guidance of Descartes, and the inseparable relationship every day makes them fall in love with each other, the princess's father, the king, was furious when he found out, and ordered Descartes to be executed, and after the little princess Christine pleaded, the king exiled her back to France, and Princess Christine was also placed under house arrest by her father. ”

Soon after his return to France, Descartes fell seriously ill, and he wrote letters to the princess every day, but Christine never received Descartes' letter because he was intercepted by the king. Descartes died of exhaustion after sending Christine a thirteenth letter with a short formula: r=a(1-sinθ). The king could not read it, and felt that there was not always a love talk between the two of them, and summoned all the mathematicians of the city to the palace, but none of them could unravel it, and he could not bear to watch his beloved daughter sullen all day, so he handed the letter to Christine, who had been sullen all day. Natalie smiled out of the corner of her eye, looking down at the figure she had just drawn.

"Yes, she immediately drew the shape of the equation like you, and she was very happy to see the figure, she knew that her lover was still in love with her, and it turned out that the shape of the equation was the shape of a heart, and this is where the heart-shaped line came from. Lu Qiujian pointed to the picture and said.

Of course, this story full of bosom friends can't stand scrutiny at all, first of all, Christine was 24 years old in 1649 instead of 18 years old; secondly, her father was the famous Gustav II, Gu Erye died in the Battle of Lüzen as early as 1632, and by this time it is estimated that even the bones in the tomb are rotten, how can there be a chance to execute Descartes; and when Lu Qiujian first read this article, the original text wrote that Christine drew this pattern in a direct coordinate system, but r=a( 1-sinθ) is obviously a polar coordinate equation, while the equation for the cardioid line in the Cartesian coordinate system should be 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).

There are more other loopholes, but as a man with normal emotional intelligence, Lu Qiujian knows that the feeling of romance is the most important thing for women, as for the truth and logic of the facts, if they don't conform to romance, then die!

So, if you hear that woman tell you a romantic story about the heart-shaped line, don't try to point out the loopholes in the story, or you will only be waiting for you.

Of course, if you have good math skills, you can also draw r=Arccos(sinθ) on the polar coordinates, x=a*(2*cos(t)-cos(2*t)), y=a*(2*sin(t)-sin(2*t)), which can make heart-shaped lines. So the image of a scholar who understands romance appears in front of the girl, and you will gain the achievement of worship +5 and favor +10, and you have taken another key step forward on the road to overthrow.

"I don't think I'm as talented in mathematics as Descartes, but I'll be happier than him, won't I?" Lu Qiujian looked at Natalie with gentle eyes and gently took her jade hand.

The equation of the heart-shaped line is actually far more than what is mentioned in this chapter, and interested friends can study it and take it to pick up girls!