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When math is witnessed in its purest form the realization can be truly amazing. Sometimes the application of mathematics can seem to be separate from the natural world but in actual fact when we take the time, math can be seen all around us. But how can we find examples of math in nature? It is as simple as opening our eyes. The majority of our knowledge of mathematics and modern science is strictly based and supported on our observations of our environment. What was once seen as the randomness of nature is now distinguished as the intricate applications of mathematics and illustrates the complexities of our natural world.

Symmetry1

Many mathematical principles are based on ideals, and apply to an abstract, perfect world. This perfect world of mathematics is reflected in the imperfect physical world, such as in the approximate symmetry of a face divided by an axis along the nose. More symmetrical faces are generally regarded as more aesthetically pleasing.

Symmetry2

Five axes of symmetry are traced on the petals of the flower, from each dark line on the petal to an imaginary line bisecting the angle between the opposing lines. The lines also trace the shape of a star.

Shapes - Perfect

Earth is the perfect shape for minimising the pull of gravity on its outer edges - a sphere (although centrifugal force from its spin actually makes it an oblate spheroid, flattened at top and bottom). Geometry is the branch of maths that describes such shapes.

Parallel lines

In mathematics, parallel lines stretch to infinity, neither converging nor diverging. The parallel dunes in the Australian desert aren't perfect - the physical world rarely is.

Shapes - Cones

Volcanoes form cones, the steepness and height of which depends on the runniness (viscosity) of the lava. Fast, runny lava forms flatter cones; thick, viscous lava forms steep-sided cones. Cones are 3-dimensional solids whose volume can be calculated by 1/3 x area of base x height.

Geometry - Human induced

People impose their own geometry on the land, dividing a random environment into squares, rectangles and bisected rhomboids, and impinging on the natural diversity of the environment.

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.

Zero - Placeholder and Number

Zero is one of the most important mathematical concepts. The idea of zero as a placeholder, eg to distinguish 303 from 33, developed in both Indian and Babylonian cultures.

Geometric sequence

Bacteria such as Shewanella oneidensis multiply by doubling their population in size after as little as 40 minutes. A geometric sequence such as this, where each number is double the previous number [or f(n+1) = 2 f] produces a rapid increase in the population in a very short time.

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.