Nature is an interesting blend of mathematics and aesthetics. The mathematics in nature has been hardwired into our brain throughout evolution. Our likes, dislikes, sense of beauty are predefined by the seemingly unimportant role of mathematics. You have probably heard of the golden ratio of faces, Fibbonacci series that is evident in the pattern in which sunflower seeds are arranged in the flower or even Da Vinci’s Vitruvian man that depicts the ratios of an ideal human body or for that matter, even the music that soothes the ear also has its roots in mathematics. To really understand why these examples are significant we must get into the math.
If one takes any term (say nth term) in the Fibbonacci series, that follows a simple rule that any term in the series is a sum of its previous two terms and divides it by the next term (say n+1 th) in the series we get a value (say m(n)). If one takes the time and actually calculates the values, they will observe that as m increases the ratio also tends to a certain value, this certain value is, you guessed it, the golden ratio (GR= 1.6180…).
This is also seen in the Vitruvian man, how, you ask? Well, Leornado Da Vinci was a man ahead of his time, he hypothesised that the ideal ratio of the distance between the foot and the navel to the distance between the head to the navel comes to about 1.618:1, which is very close given the tools he had at his disposal. This is also seen in a lot of faces, the length to breadth ratio of the face, the ratio of the distance between the eyes to the width of the face and so on, all of them come out to be close to the golden ratio.
Not only this, but ancient Greeks used this same ratio to build the great Parthenon where the length of the column to the width of the roof comes out to be the golden ratio. Even modern structures have this ratio inherently built into the system to look more appealing to every gazing eye.
Beauty and mathematics have been intertwined since time immemorial, and all the examples presented are a testament to this. As rightly said by Proclus “Wherever there is number, there is beauty”, one must fully appreciate this merger and must learn to appreciate the mathematics of beauty and the beauty of mathematics.