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Maths and nature
By May Lin Xiu Lian Lin (P2898) on Tuesday, September 12, 2000 - 11:38 am:

I would like to ask if there are things in the nature that are related to maths.

By Neil Morrison (P1462) on Tuesday, September 12, 2000 - 03:59 pm:

Just about everything

By Tony Chi Kin Ho (P1942) on Wednesday, September 13, 2000 - 05:22 pm:

Good answer. I completely agree.

By Marcus Hill (T3280) on Thursday, September 28, 2000 - 12:38 pm:

An easier question to answer would be "are there any things in nature which are not related to maths?"

By Alex Barnard (Agb21) on Sunday, October 1, 2000 - 11:07 pm:

Okay... well how about we actually give some examples here rather than just saying 'everything'!

There is a very famous sequence of numbers in mathematics called the Fibonacci numbers. It starts off 1,1,2,3,5,8,13,21,34,55,... Where, to work out the next number all you do is to add the previous two. So 55=34+21 and the next number is going to be 55+34 = 89.

This was written down by an Italian mathematician (Fibonacci) to very simply describe how rabbit populations increase. So the numbers represent how big the population is. As you can see it starts off slowly but gets faster and faster. This is an example of exponential growth and can be found in many biological systems when the organisms are not under pressure for space. For example the population of the world is currently growing like this although soon it will begin to slow down because there simply won't be enough space for everyone to live. There is a lot of active mathematical research into describing nature using mathematical models (eg. describing how disease spreads).

Second example. If you pick two terms in the Fibonacci sequence that are next to each other (eg. 89 and 55) and look at the larger divided by the smaller 89/55 = 1.618. Then if you do this for bigger and bigger terms you should see that it seems to be getting closer to a number starting 1.618034. This number is called the golden ratio and also turns up lots in nature. For example, it has long been known in western art (and probably in eastern but I don't personally know) that the most pleasing place to put a person in a picture is not exactly in the centre but slightly closer to one side. The exact amount being determined by the golden ratio. Now, why this is I don't know but I've seen results from many studies where you ask someone to say which photos they prefer and the golden ratio always comes out on top. Shells of snails and certain sea creatures have spirals that decrease in size almost exactly at the rate of the golden ratio.

The Fibonacci numbers themselves also turn up in nature. On a plant there are often several things which come together at one place -- eg. tree branches split into 2 or 3, leafs on a plant start at the same place. And, almost always the number of things that come together is a fibonacci number. So, 3-leaf and 5-leaf plants are common whereas 4-leaf ones are not.

So these are all examples of one mathematical thing which turns up in nature. There are many more that turn up and this isn't too much of a surprise. Mathematics is not totally separate from our surroundings - many definitions in mathematics are inspired by things we see.

AlexB.