Maths in nature
"The laws of nature are but the mathematical thoughts of God"
- Euclid
Mathematics is everywhere in this universe. We seldom note it. We enjoy nature and are not interested in going deep about what mathematical idea is in it. Here are a very few properties of mathematics that are depicted in nature.
SYMMETRY

Symmetry is everywhere you look in nature .

Symmetry is when a figure has two sides that are mirror images of one another. It would then be possible to draw a line through a picture of the object and along either side the image would look exactly the same. This line would be called a line of symmetry.

There are two kinds of symmetry.

One is bilateral symmetry in which an object has two sides that are mirror images of each other.

The human body would be an excellent example of a living being that has bilateral symmetry.

The other kind of symmetry is radial symmetry. This is where there is a center point and numerous lines of symmetry could be drawn.
The most obvious geometric example would be a circle.

Shapes
Sphere:

A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball.

The shape of the Earth is very close to that of an oblate spheroid, a sphere flattened along the axis from pole to pole such that there is a bulge around the equator.

The wee electron has gotten its most thorough physical examination yet, and scientists report that it is almost, almost a perfect sphere. Researchers at Imperial College London have determined the electron is just 0.000000000000000000000000001 centimeter off from being perfectly round.
Bubbles are also a common example of a near perfect example of a sphere
Hexagons:

Hexagons are six-sided polygons, closed, 2-dimensional, many-sided figures with straight edges.

For a beehive, close packing is important to maximise the use of space. Hexagons fit most closely together without any gaps; so hexagonal wax cells are what bees create to store their eggs and larvae.

Cones:

A cone is a three-dimensional geometric shape that tapers smoothly from a flat, usually circular base to a point called the apex or vertex.

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.

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. Spirals are common in plants and in some animals, notably mollusks. For example, in the nautilus, a cephalopod mollusk, each chamber of its shell is an approximate copy of the next one, scaled by a constant factor and arranged in a logarithmic spiral.Many examples of the Fibonacci spiral can be seen in nature, including in the chambers of a nautilus shell.
Pi and circles
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.

There are many near perfect cirles in nature. For example- Saturn’s rings
A closeup of a human eye reveals that the pupil is almost a perfect circle.
According to some the arc of a rainbow is the second closest thing to a perfect circle in nature after a ripple

"The closest thing to perfect circles in nature is probably circular wave patterns on a pond or puddle after a raindrop falls on it.” Even when a noncircular object is thrown into water, the resulting ripples will form in concentric circles. Initially, the ripples expand accordingly to the object's shape. But as they spread farther outward, curves fill in the uneven spaces, leaving the ripples to "morph" into circular shapes

Fibonacci sequence
Rabbits, rabbits, rabbits. Leonardo Fibonacci was a well-travelled Italian who introduced the concept of zero and the Hindu-Arabic numeral system to Europe in 1200AD. He also described the Fibonacci sequence of numbers using an idealised breeding population of rabbits. Each rabbit pair produces another pair every month, taking one month first to mature, and giving the sequence 0,1,1,2,3,5,8,13,... Each number in the sequence is the sum of the previous two.

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(n)] produces a rapid increase in the population in a very short time.

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.

1. www.abc.net.au/science/photos/mathsinnature/blank.htm 1. malini-math.blogspot.com/2010/08/maths-and-nature.html‎ 2. en.wikipedia.org/wiki/Patterns_in_nature‎ 3. www.vedicmathsonline.com/maths%20in%20nature.html