Written by Kirsten Macdonald

Why do bees buzz? What does maths have to do with sunflowers and the many beautiful fractal patterns of our world? 


A favourite book in our home held some wonderful clues to the mysteries of our hidden world. Critically acclaimed science-fiction author Ian Stewart is a British mathematician. He is Emeritus Professor of Mathematics at the University of Warwick, England. 

He has published more than 120 books, with an extensive list of impressive titles to wet your Harry Potteresque whistle, such as 

Professor Stewart’s Cabinet of Mathematical Curiosities

Why Beauty Is Truth: A History of Symmetry 

How to Cut a Cake: And Other Mathematical Conundrums- 

Professor Stewart’s Hoard of Mathematical Treasures

and he even has an award-winning app,  Incredible Numbers by Professor Ian Stewart

We are going to focus on The Beauty of Numbers in Nature.  Ian Stewart’s preface to his masterpiece is a touching genesis.


“When I was six, a friend showed me some curious little five-pointed stars that he had found on the beach…I became aware of a deep mystery: why does nature produce so many patterns?”

Stewart’s language maintains the mystery in the metrical, but the plurality of simple explanations and anecdotes make for fascinating reading. A feast for the mind that is anything but mundane; I would like to reflect on a selection of favourite chapters. 

Many shapes in our world typically look flat-faced in geometry. Not the spiral. 

Spiral Swirls 


“One of the favourite patterns of life, in fact, is based on curves- the spiral…Spiral shells appear way back in the fossil record, and one of the most common. The shell is formed by a soft bodied organism, for protection. As the creature’s size increases with age, it outgrows its existing chamber and builds an extension into its house.” 


Chambers and hidden secrets. It is no wonder Sir Terry Pratchett awarded Stewart Honorary Wizard of the Unseen University. 


“On land, snails build similar shells. Snail shells and indeed many seashells, often coil into the third dimension. Of course, the shape of the shells is always three dimensional: what I mean is that the “core of the spiral”, the line that runs along the centre of the chambers, ceases to lie in a plane and starts to curl into a third dimension of space.” 


I will never step on a garden snail again. An architect of a logarithmic spiral, powering into itself – not all it seems in our microworld. 


The Fibonacci Flowers


Fibonacci, the son of a custom’s officer, was a numbers man. His problem solving around rabbit populations in 1202 spawned mathematical patterns that would revolutionise thought. In basic terms; where after the first two numbers, each number is obtained by adding together the previous two numbers in the sequence. eg 1,1,2,3,5,8,13,21,34,55 – each number in the sequence is the sum of the previous two numbers. 

 Stewart observes: 

“Fibonacci numerology and spiral geometry are surprisingly common. They suggest that plant growth obeys simple but subtle mathematical rules, which lie somewhere in the interface between dynamics, geometry and arithmetic… Fibonacci numbers have penetrated deep into the mathematical psyche as an apparent endless source of inspiration and wonder…these numbers occur in the spiral structures many use to arrange their seeds. Fir cones are a good example. The scales on fir cones are typically arranged in two families of intertwined spirals, and each family contains a Fibonacci number of spirals…the seedhead of a sunflower displays these spirals in a gloriously regular pattern. Lillies have 3 petals; buttercups have 5, delphiniums often have 8, corn marigolds have 13, asters have 21.” 

photo: Ponderings Australia

Like your veggies? 

Stewart states:

“The same numerology can also be seen in cauliflower, which we usually think of as featureless lumps of soft white tissue. On closer inspection, we find that the lumps are arrayed in beautiful spiral swirls. Sometimes the eye of a mathematician can see things that other eyes miss…Broccoli Romanesco, each unit of the spiral is itself a spiral, a miniature version of the entire plant.” 


photo credit; Ian Stewart The Beauty of Numbers in Nature

A golden angle is achieved with spiral growth which impacts things such a seed spacing, protection, growth and efficiency of survival. 


Ponderers we are consuming an intricate pattern of design, not just nutrients! The microcosmos in our backyards and onto our plates is extraordinary.


JAX Tyres for Ponderings

The Magic of Why A Bee Buzzes


“Most of what goes on when a creature flies is invisible to the eye because air is transparent. A bird in flight spins of a regular pattern of vortices, swirls of air spinning off from the trailing edges of its wings. The bird exploits these vortices to gain lift. Only recently have human engineers understood this particular trick, but the birds have known for a hundred million years.”

“We know how bees and other insects pull off their counterintuitive feat. Their wings move upward until they almost touch. When they beat downward, the sharp edge creates a leading-edge vortex. For reasons we don’t fully understand, this vortex remains ‘stuck’ to the top of the wing, generating lift, and spirals along it until it is shed at the wingtip. This method requires small wings that beat very rapidly, which is why bees buzz. And it’s why the flying pig will remain a metaphor for the incredible.” 

Don’t uyou wish we could see air in colour?


Fascinating world of fractals


“A Fractal is a geometric shape that has a fine structure no matter how much you magnify it…Nature’s fractals are extremely intricate, but they fuzz out on the atomic scale. A mathematician’s fractals are infinitely intricate and never fuzz out, no matter how closely you look.” 

“Rivers are trees of flowing water-the main river is like a trunk; its larger tributaries are branches, the tiny streams up the hills are the twigs. The water then ends in the river and erodes the land into fantastic treelike patterns. Our entire planet is a fractal. If you are a geologist.” 

The Beauty of Numbers in Nature is 223 pages, explaining every pattern imaginable, cascading into a presentation of deep philosophical questions about the foundations of physical law, the nature of space, time and matter, and the shape and history of the universe. Order in chaos, time travel and the realms of understanding is more than enough to nibble on. With beautiful pictures, this is the perfect coffee table book and will have you pondering. 

“When nature keeps reusing the same catalogue of patterns, the wise scientist pays attention.” – Ian Stewart

For those homeschooling, we have also sourced a wonderful list of resources to help kids explore science and the mico-world! 



How Mathematicians Think About Patterns – Professor Ian Stewart

Fibonacci for kids 


Professor Ian Stewart is an active research mathematician with over 200 published papers, and currently works on pattern formation, chaos, network dynamics, and biomathematics. He lives in Coventry, UK, and is married (49 years and counting) with two sons, three grandchildren, and one great-grandchild. He is also a critically acclaimed science-fiction author. He has partnered on the award-winning Discworld series with Sir Terence (Terry) Pratchett OBE, an English author of fantasy novels, especially comical works. 




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