maths in nature

(Image: Darren Osborne) Pi

Any circle, even the disc of the Sun as viewed from Cappadoccia, central Turkey during the 2006 total eclipse, holds that perfect relationship where the circumference divided by the diameter equals pi. First devised (inaccurately) by the Egyptians and Babylonians, the infinite decimal places of pi (approximately 3.1415926...) have been calculated to billions of decimal places.



Fractals

Many natural objects, such as frost on the branches of a tree, show the relationship where similarity holds at smaller and smaller scales. This fractal nature mimics mathematical fractal shapes where form is repeated at every scale. Fractals, such as the famous Mandelbrot set, cannot be represented by classical geometry.


(Image: iStockphoto) Fibonacci spiral

If you construct a series of squares with lengths equal to the Fibonacci numbers (1,1,2,3,5, etc) and trace a line through the diagonals of each square, it forms a Fibonacci spiral. Many examples of the Fibonacci spiral can be seen in nature, including in the chambers of a nautilus shell.


(Image: NASA/JPL-Caltech/CfA) Infinity

Is one infinity bigger than another infinity? The size of all natural numbers, 1,2,3..., etc., is infinite. The set of all numbers between one and zero is also infinite - is one infinite set larger than the other? The deep questions of maths can leave you feeling very small in a vast universe.



(Image: Wilson Bentley) Uniqueness, proofs

Proofs are the tools used to find the rules that define maths. One such proof is by counter example - find one duplicated snowflake, like Nancy Knight of the US National Center for Atmospheric Research did while studying cloud climatology, and the theory of snowflake uniqueness disappears into the clouds. The theory may have originated from Wilson Bentley's extraordinary feat photographing over 5000 snowflakes in the 1930s. He found no two alike.


(Image: iStockphoto) Golden ratio (phi)

The ratio of consecutive numbers in the Fibonacci sequence approaches a number known as the golden ratio, or phi (=1.618033989...). The aesthetically appealing ratio is found in much human architecture and plant life. A Golden Spiral formed in a manner similar to the Fibonacci spiral can be found by tracing the seeds of a sunflower from the centre outwards.



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