*Our perception of beauty is cultural, to some degree. However, there is an underlying appreciation of symmetry, order and the natural rhythms of nature, some of which are captured in mathematics.*

Early on, mathematicians identified an interesting series - start with zero; then add one. Now, each subsequent number of the series is built from a simple algorithm - the sum of the sum of the two previous numbers, plus the most adjacent previous number, or:

0 + 1 = 1, 1 + 1 = 2, 2 + 3 = 5, etc.

This yields the following number series:

0, 1, 1, 2, 3, 5, 8, 13, 1, 34, 55, 89, 144, etc.

Often called the Fibonacci series after the Italian mathematician who popularized the concept in 1200 C.E., the concept goes back further to Indian mathematics.

Turns out, this is an amazing sequence that seems to underlay the natural growth patterns in nature. If you create a spiral, based on squares that follow the series - squares with a side of one, then 2, then 5, then 8, etc. - you get an approximation of the Golden Section that artists have used since the Renaissance to develop harmonious compositions, dividing the space into Golden Section proportions.

It also underlies the natural ratios that lead to harmony in music, to the divisions of space in architecture, to the fractal geometries of ferns, snowflakes, and rivers.

So, to some degree, our appreciation of beauty relates to an appreciation of the visual or aural evidence of the logic of mathematics.

“Music is liquid architecture; **Architecture is frozen music**.” ― Johann Wolfgang von Goethe