A connection between Mathematics and Love: the story goes that a very shy mathematician had fallen in love with a girl but did not dare to tell her. In stead he wrote her a letter with only the following formula: $$y=\pm \sqrt{25-x^2} -\frac{3}{|x|+1}$$ If she was really interested he counted on her drawing the graph of the formula. How the story ended no one knows ...

 

So how does one construct such a formula? The first part of the formula (the square root without the fraction) is an ellipse: $(3x)^2+(5y)^2=15^2$. Now to get a heart shape the top and bottom of this ellipse must be somewhat lowered and this is accomplished by adding the fraction which is really an adjusted orthogonal hyperbola, $y=\frac{1}{x}$, in such a way that it connects to the ellipse. Desmos is a fantastic tool to illustrate this and hence explaining graphs, functions and and a bit of analytical geometry.

A connection between mathematics and love:

The story goes that a very shy mathematician had fallen in love with a girl, but he did not dare to tell her. Instead, he wrote her a letter with only the following formula: $$y=\pm \sqrt{25-x^2} -\frac{3}{|x|+1}$$

If she was really interested, he counted on her drawing the graph of the formula. How the story ended no one knows ... 

So how does one construct such a formula? The first part of the formula (the square root without the fraction) is an ellipse: $(3x)^2+(5y)^2=15^2$. Now to get a heart shape the top and bottom of this ellipse must be somewhat lowered and this is accomplished by adding the fraction which is really an adjusted orthogonal hyperbola, $y=\frac{1}{x}$, in such a way that it connects to the ellipse. Desmos is a fantastic tool to illustrate this and hence explaining graphs, functions and and a bit of analytical geometry.