Last October, I took my son around Palladio's Villa Emo in northern Italy. He's no fan of architecture - the dullest hours of his childhood have been spent in old cathedrals. But this visit elicited a surprising burst of enthusiasm, for an interesting reason: maths.
The main hall at Villa Emo is a square. The symmetrical rooms to either side share its length, but they are squeezed down to golden-ratio rectangles. These, in turn, lead to smaller side lobbies, while the rooms flanking the portico become cubes with a "golden" proportional relationship to the original hall. Seen this way, Villa Emo becomes an extraordinary 3D matrix of intertwined shapes: a building that is also a mathematical formula. Or, perhaps one should say, a mathematical formula that is also a building, because my son's discovery was not so much an exciting new way into architecture as a new way into maths.
All buildings involve maths in one way or another. Many, including the Parthenon in Greece and the Taj Mahal in India, use complex mathematical proportions. Some use maths symbolically, like the clusters of windows in Gothic cathedrals (three for the trinity, six for the days of the Creation). A good few - such as Turkey's Hagia Sophia and the Sydney Opera House - are intricate compositions of shapes and spaces that can only truly be described through mathematics.
Pattern, proportion, Pythagoras
So could buildings work in the classroom as a way of making maths' complexities visible? Proportions show how size and number can fall into patterns. Surveying space brings maths into play as a way of capturing real things around us. Measurement teaches children to manipulate numbers, and checking angles takes a class to trigonometry and Pythagoras. If teachers are looking for a series of right angles to demonstrate numbers' magic, they need only look around their own classroom.
All this sounds like an enjoyable end-of-term lesson, but perhaps there is more to it than that. An Australian maths teacher remarked to me recently how different maths practice was at home from the methods he encountered in Britain. In Australia, he told me, maths was taught visually, using more trigonometry and geometry, and less of the number work that condemned me to the bottom half of the class. Mathematics doesn't need to be an abstract pursuit. Some mathematical concepts have always been open to visualisation. Lacking algebra, ancient Greek mathematics relied heavily on geometry.
Although it would be easy to descend into oversimplifications about visual people and abstract thinkers, there's still an opportunity to be seized here. Some aspects of mathematics can be "seen", as my son and I discovered in Villa Emo. Some children will find that this opens doors that would otherwise be closed to them.
Brick by brick
Maths may not be the only subject to benefit from a closer look at buildings. The Farrell review of architecture and the built environment in the UK recently recommended that both subjects become part of the school curriculum. And so they should. A building is a work of art and a mathematical construct. It is also a space for living, a stage for human drama, a physical structure withstanding wind, snow and its own weight, a machine to pump heat, air and water to its occupants (and take their waste away), a financial investment, a tiny chunk of city or landscape and a fragment of surviving history.
There may be nothing unique about buildings in these regards - many large artefacts could be analysed from the same points of view. But buildings are everywhere. Their diversity in size and age, function and construction technique, make them a fascinating document of human activity. They are the most widespread, varied and readily available man-made resource that we have.
In fact, when you think about it, it is hard to find a subject that could not be explored through buildings. Imagine a shared school day at a local library or town hall - or even in the school itself. When was it built, and why? Old maps will give the site's history. If it was paid for by an education act, then who campaigned for that act? If the previous building was bombed, who dropped the bomb and why? The maths group can triangulate corners and survey them. The physicists can lift the floorboards to see how they stay up, and so on.
Students could also learn from conceiving their own buildings. Architecture is a complex mixture of pure creativity (what does it look like?), contextual analysis (where is the sun? How do pedestrians reach it?) and problem-solving.
The latter comes very close to the pure logic of an intelligence test - take, for example, the following challenge: provide three square classrooms of 65sq m, each with a store of 10sq m and an opening on to an assembly space of given dimensions. Everything must fit into a rectangle - now draw it.
If it does not catch on in all subjects, then maths teachers at least should see the benefits of architecture in all that they do. Isidore of Miletus, designer of Hagia Sophia, was a mathematician. His collaborator, Anthemius of Tralles, was a professor of geometry. The buildings that surround us were engineered through mathematics, measured and valued through numbers, and made beautiful through proportion. Architecture is, in the end, a mathematical art. For teachers of mathematics, there could be no better resource.
Patrick Dillon is the author of The Story of Buildings, a children's book published by Walker Books, pound;16.99