Terms such as Built Environment and Maths don’t incite images of beauty in my mind. Just like ‘Built Environment’ gives me images of a concrete jungle, Mathematics makes me think of a jungle in its own way too, a tangle of theories and equations; especially for someone who never felt very good at maths whilst in education. An Amazonian-esque rainforest that makes me nervous to explore, especially without a guide.
Bob Marley describes the concrete jungle as a place “where living is harder” in his 70s hit of the same name and while more recently Alicia Keys referred to New York City as a “concrete jungle where dreams are made of” she also described a place of struggle. This description perfectly sums up my experience with maths, and in particular maths anxiety. For me, maths has been a place of struggle, at times, but one I knew that could transform my world if I could crack it; much in the way New York becomes a place of glitz and glamour in all the movies when the struggling actor becomes successful.
So, what has any of this to do with the Beauty of Maths?
Well, many of the buildings we see in our built environment are based on mathematical principles, so when we say that Maths is everywhere – we really do mean everywhere. We as humans have just become so accustomed to it that sometimes we don’t even recognise it as maths anymore.
In the last year, I have done a lot of personal development around Maths and in doing so, have learned some really great things about maths and how it is literally everywhere. I was even shocked to learn about the maths I do everyday in my role as a Construction Planner, that I hadn’t recognised as Maths because it was so every day.
In doing so, I have learned that there is so much maths around us, all the time, we are literally surrounded by it and many of us may not even notice it or recognise it as even being maths. I have also learned that much of it, can really be very beautiful if you stop long enough to notice.
I’m focusing on the Built Environment because that is where my experience lies but the beauty of maths can be found everywhere. It is in nature, even as close as our human bodies. And it is from our human bodies that one system of architectural proportion was constructed.
Le Corbusier, a Swiss-born French Architect who is regarded as one of the pioneers of modern architecture created his ‘Modulor’ from human measurement.
Modulor is an anthropometric scale of proportions used in Le Corbusiers architecture and was codified into two books. It is based on a man with his arm raised in the air. The system is based on human measurement, the double unit, the golden ratio, and Fibonnacci numbers with Le Corbusier him self describing it as a “range of harmonious measurements to suit the human scale, universally applicable to architecture and to mechanical things". He used this scale in his designs for numerous buildings.
The Golden Ratio (found in a rectangle whose sides are 1: 1.618) was discovered by Euclid, an Ancient Greek Mathematician who is considered the father of Geometry, a Geometer and Logician. There is a relationship between this ratio and the Fibonacci numbers, but it wasn’t evident that Fibonacci has realised this this link. It was Scottish Mathematician Robert Simson in the seventeenth century that proved the link, but even then, not fully.
Mark Barr an American Mathematician in the early twentieth century, gave the Golden Ratio the name Phi (φ) named after the great sculptor Phidias as it was believed he used the ratio in many of his sculptures and the architectural design for the great Parthenon.
The Golden ratio is seen in paintings, such as the Mona Lisa, the Great Pyramids of Egypt and even our human bodies. It is also replicated in nature in the form of seashells, chameleon tails, ocean waves, snail shells, flowers, whirlpools, pinecones and even spider webs and that is just a few examples.
It is used in these applications as it is thought be aesthetically pleasing.
Of course, all buildings are created using mathematics in design and in the engineering aspects to determine how strong the structures need to be, but these are the obvious applications.
Buildings that incorporate the Golden Ratio include:
Parthenon, Athens, Greece
The Core at Eden Project in Cornwall – the main structure also incorporates Geodesic domes (structures made using hexagons and pentagons connected to make a dome shaped structure) and phyllotaxis which is the mathematical basis for the growth of plants (therefore we see the golden ratio in plants).
In the built environment, we can also see many excellent representations of mathematics in action to create fantastic structures that last the test of time and fashion.
Some of brilliant examples of mathematically brilliant constructions include:
· The Pyramids of Giza, Egypt a mathematical marvel uses the golden ratio but also in cubits (the first ever recorded unit of length) it is 365.24 which is the number of days in a year. The perimeter divided by twice its height is equal to Pi (3.14) and the Kings Chambers are based on Pythagoras’ Theorem (3, 4, 5)
· The Gherkin, London used both parametric modelling (statistical modelling) and the maths of turbulence to create its unique shape.
· The Taj Mahal, India uses symmetry so that the prayer towers can be reflected perfectly into the body of water in front of the building, making it a much-photographed image.
· The Sagrada Familia, Spain uses Hyperbolic Paraboloid structures (quadratic surfaces) for some of the feature facades and Gaudi also used a Magic Square within the Passion façade – an arrangement where the numbers in all columns, rows and diagonals add up to the same sum: in this case, 33.
· Effekt Bridge, Denmark features a spiral around a hyperboloid so that visitors can view the natural surroundings without detrimentally impacting it.
· Tycho Brahe Planetarium, Denmark is an ellipse shaped construction.
· Lideta Mercato, Ethiopia is a shopping centre designed to represent patterns found on Ethiopian dress. The windows are based on fractal designs. Fractals are never-ending patterns and are self-similar at different scales.
· Villa La Rotonda, Italy is an exceptionally symmetrical building the design of which influenced architecture for the design of the White House.
· The Sage Music Centre, Gateshead, UK is used using 27 sections of a torus. A torus is the mathematical name for a doughnut shape.
· Grand National Rollercoaster, Blackpool Pleasure Beach is constructed in the representation of a mobius strip. A Mobius strip or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist
And if you look even inside your own home, you may find examples of maths in action in the form of truss designs for your roof structures, tessellation (or tiling patterns) in bathroom, kitchen’s or floor patterns, which are made from many geometric shapes connected together.
In your everyday, you may pass by bridges and buildings and see the shapes that make up our built environment, but you maybe don’t give much thought to the Maths that goes on behind creating such iconic and impressive structures.
Now you can understand that because of the beauty of maths in nature and in our own human bodies, the principles behind the amazing structures that make up our beautiful built environment were founded and just like New York, to the successful actor, you will see wonder and amazement in the concrete jungles in which you roam.