Maths in nature

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Scouts have a close relationship with science; it’s well documented that we produce engineers, astronauts and all sorts of men and women who use maths often. However, some Scouts likely have a less close relationship with maths. Outside of classrooms, maths comes alive in a way it doesn’t on paper or a whiteboard. Maths is in the clothes we wear, the roads we cross, the buildings we live in. Maths is all around us.

14 March marks Pi Day, a celebration of the mathematical constant ‘Pi’. Pi in a number is about ‘3.141…’ or ‘three and a bit’. Before being mixed up with dessert, Pi was originally defined as the ratio of a circle’s ‘circumference’ – the length of the circle – to its ‘diameter’ – the length from one side of a circle to the other. Beyond imaginary circles, maths unlocks the secrets behind much of nature’s designs; here we examine some of the maths we can see in the natural world around us.

Symmetry and fractals

Symmetry simply means reflection. If something has a line of symmetry, then if you were to put a mirror right on that line, it would look like a window to the other half of the object because both halves would look the same. Symmetry appears all over our world, from our faces to our flowers.

One special example of symmetry is the humble snowflake. Our delicate winter visitors are known to each be unique, but one unusual thing they all have in common is their six-fold symmetry. When drawing a line of symmetry through the middle of a snowflake, you can do so five more times and get a different line of symmetry each time.

We don’t know why snowflakes arrange themselves symmetrically yet, but being able to see that they do leads us to asking the kind of questions that will eventually tell us more about our world. The symmetry of human and animal faces is useful for many reasons, such as having eyes and ears on either side letting us see and hear our surroundings.

A fractal can be thought of as simply a pattern with a special kind of symmetry. Patterns in general have one part which is repeated over and over again. Fractals are a ‘pattern within patterns’, where each part of the fractal looks like the overall fractal.

The clearest visual example of this in nature can be eaten for dinner. Romanesco broccoli would be an especially eye-catching piece of vegetable, if you ever get a chance to eat it. Each floret of this vitamin rich piece of broccoli looks like the whole piece, and if you have a magnifying glass then you can see how each floret of the florets follow the same pattern.

Fractals can be seen all over nature if you look closely. The way a branch breaks off into multiple twigs is very similar to the way a tree breaks off into multiple branches. The human brain even follows a similar sort of pattern. Nature uses this branching system to efficiently distribute its resources, like oxygen in our bodies and brains, or water and nutrients across branches and leaves.  

Sequences and ratios

A sequence in maths can be thought of as an ordered list, where every item on that list follows certain rules. A famous example is the Fibonacci sequence, where each item on the list is the previous two added together. The sequence traditionally goes ‘1, 1, 2, 3, 5, 8, 13, 21, 34, 55…’ and so on, however it could begin from any two numbers and go from there, such as ‘3, 10, 13, 23…’ and so on.

The special thing about this sequence comes from something called a ratio. A ratio can be best explained by an example, take the numbers eight and four. They have the ratio two to one, because there are two fours in eight. The ratios of a Fibonacci sequence, when you read far enough down the list, become a special number called the golden ratio, or ‘Phi’, which is approximately 1.618.

Phi, like Pi, is an irrational number, which are numbers which can’t be expressed as a simple fraction. When written as decimals, they can’t be written completely, which is why we use symbols to express them.

This sequence and ratio appear in nature’s designs all the time. Flower enthusiasts are aware that lilies, roses, buttercups, and many other plants have a Fibonacci number of petals, like three, five, eight, and so on.

Sunflowers have seed spirals which add up to a Fibonacci number. They have 55 clockwise spirals and 89 anticlockwise spirals. The reason they do this, scientists theorise, is because of efficiency. Flowers can pack the maximum number of seeds if each seed is separated by an irrational numbered angle. Pineapples and pinecones also follow this sort of design, and the Fibonacci spirals can be seen on shells in the ocean as well.

Leaves are known to do this as well, in a process called phyllotaxis. This word simply means the arrangement of leaves on a plant stem. The ratio they arrange themselves at as they jut out from stems and branches, is also the golden ratio.

The reason for them doing this has to do with efficiency, as do most of nature’s designs. If leaves jut out at irregular intervals, they maximise the amount of sunlight they receive from the Sun.

Maths is often used by engineers, economists and many other people to work out the most efficient way to do something. The delicate ecosystem of our planet has used the power of maths for this exact same reason. Our universe is incredibly complex; with maths, a keen eye and a sense of adventure, there is no limit to the amount we can learn about it.

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