Eye of God

Recently I was fascinated by the curve generated using golden ratio. Just to get an intuition of the golden ratio let’s consider the following image.

We have sections of the length 1, x and (1 - x) so that

$${x \over 1 - x} = {1 \over x}, x > 0$$

From here we find

$$x = {\sqrt{5} - 1 \over 2}.$$

Now let’s consider a rectangle with sides x and 1, if we cut a square of side x we get another rectangle with the same ratio of sides because of the first equation. And if we draw a quarter of a circle in each square we’ll get this beautiful picture.

(Disclaimer: the image is generated by JavaScript right now, browser compatibility was not considered)