I love words but hate numbers. But recently I read material that I found fascinating which suggests mathematical rules underpin the shapes and patterns of the natural world to a far greater extent than previously realised.

Some of the work isn’t that recent because it was Leonardo da Vinci who suggested all branches of a tree at every stage of its height when put together are equal in thickness to the trunk — the squared diameter of a tree’s trunk is equal to squared sum of the diameters of its branches.

I find it rather incredible, but Leonardo’s formula has been found to be precisely correct. But until last year nobody really knew why. Then a French physicist called Christophe Eloy, who is an expert in fluid mechanics and the way air flows around objects, built a sophisticated computer model which demonstrated Leonardo’s formula offered the optimal solution to the problem of withstanding high winds.

So engineers and architects struggle to calculate wind loads on tall buildings and bridges using the most sophisticated tools and methods and trees had the whole thing figured out millions of years ago.

The term ‘fractal’ was first coined by the the French-American mathematician Benoit Mandelbrot. They are described as ‘self-similar’ patterns of complexity, increasing with magnification, which if divided into parts give you a nearly identical reduced-size copy of the whole —- and that may mean more to you than it does to me.

But quite recently a British mathematician called Michael Barnsley demonstrated that the shape of a typical fern frond is, in fact, a fractal and that fractal patterns occur widely in nature.

Then there are Fibonacci Sequences. If you want to know more about them I’ll politely direct you to Google. But my understanding is that they are sequences of numbers in which each number is created by the sum of the two preceding it. So 1, 2, 3, 5, 8, 13 is a Fibonacci Sequence.

But Fibonacci sequences govern many shapes in the plant world, including the number of petals a flower has, how its seeds are arranged and where its leaves sprout along its stem. For example, a chicory flower has 21 petals, an undamaged daisy has either 34 or 55, lilies have three and buttercups five. There are hardly any flowers with four petal because that isn’t a Fibonacci number.

I should have tried harder with the maths when I was at school.

Nature Table

There are hundreds of species of oak in the world but the Irish national tree is the sessile oak and it’s undoubtedly native.

The other species you are likely to come across in the wild in this country is the pedunculate oak, which is probably native.

Sessile means sitting and pedunculate means dangling. This refers to the acorns which sit on the twigs in the first species and dangle down on stalks in the second.

Unfortunately acorns are only produced by mature trees, and this doesn’t happen every year, so they are not a very useful identification tool. The leaves of sessile oaks tend to have much longer leaf stalks than those of pedunculate oaks and this is much more useful because, even in winter, there tend to be dead leaves at the base of the tree. Sadly they do hybridise and the hybrids are fertile.

So sometimes it takes a geneticist to unravel what’s happening and the lay person just has to label them oak trees.

— Dick Warner