ALPHABETTI spaghetti: now there was a name to conjure with when I was a kid. Succulent little pieces of pasta, each shaped into a letter of the alphabet, served up in a can with lashings of tomato sauce. Delicious, nutritious – and best of all they made playing with your food undeniably educational.
Some thirty years on, in an upscale Italian restaurant near the London offices of Â鶹´«Ă˝, I decide against sharing this reminiscence of family mealtimes with my lunching partner. George Legendre doesn’t look quite the type. For one thing, he is French, and possibly indisposed to look kindly on British culinary foibles. For another, he is an architect, designer and connoisseur of all things pasta. In fact, he has just compiled the first comprehensive mathematical taxonomy of the stuff.
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Quiz: Can you match the pasta with its mathematical equation?
According to a by the charity Oxfam, pasta is now the world’s favourite food. Something like 13 million tonnes are produced annually around the globe, with Italy topping of both producers and consumers, according to figures from the International Pasta Organisation, a trade body. The average Italian gets through 26 kilograms – that’s the uncooked mass – of pasta each year.
The plate of paccheri in front of me seems positively modest by comparison. To my untrained eye, it consists of large, floppy and slightly misshapen penne. I might not be too wide of the mark. “If you look carefully, there are probably only three basic topological shapes in pasta – cylinders, spheres and ribbons,” Legendre says.
“There are probably only three basic topological shapes in pasta: cylinders, spheres, and ribbons”
Nevertheless, that simplicity has, in the hands of pasta maestros throughout the world, spawned a multiplicity of complex forms – and inspired many a designer before Legendre (see “Primi piatti”). It was a late-night glass of wine too many at his architectural practice in London that inspired Legendre, together with his colleague Jean-Aimé Shu, into using mathematics to bring order to this chaotic world.
“The first thing we did was order lots of pasta,” Legendre says. Then, using their design know-how, they set about modelling every shape they could lay their hands on to derive formulae that encapsulate their forms. “It took almost a year and almost bankrupted the company,” he says.
For each shape, they needed three expressions, each describing its form in one of the three dimensions. This provides a set of coordinates that, plotted on a graph, faithfully represents the pasta in 3D. The curvaceous shapes of most pasta lend themselves to mathematical representations mainly through oscillating sine and cosine functions.
For some pastas, the right recipe was obvious. Spaghetti, for example, is little more than an extruded circle. The sine and cosine of a single angle serves to define the coordinates of the points enclosing its unvarying cross- section, and a simple constant characterises its length. Similarly, grain-like puntalette are just deformed spheres. The sines and cosines of two angles, together with different multiplying factors to stretch the shape out in three dimensions, supply its mathematical likeness. “The compactness of the expression is beautiful,” says Legendre.
Other shapes were harder to crack. Scrunched-up saccottini, for example, looks for all the world like the of a hyperbolic plane that adorns my desk at Â鶹´«Ă˝, and its shape is captured by a complex mathematical mould of multiplied sines and cosines. Simple features such as the slanted ends of penne take some low modelling cunning, involving chopping the pasta into pieces, each represented by slightly different equations.
Sharp inflections, such as the undulating crests of the cockscomb-like galletti (shown above), are tricky too, though trigonometric functions again turn out to be the best tools for the job: raising sines and cosines to a higher power constricts the smooth, oscillating shape of the function into something approaching a spike. A similar technique can be used to broaden out the function into something approaching a right angle – a trick Legendre dubs an “asymptotic box”. “Saying to colleagues you’re developing mathematics to make a box makes them think you’re crazy,” he says.
In the end, he had a compendium of 92 pasta shapes, each exactly modelled and divided into categories according to the mathematical relationships revealed between them – some obvious, some less so. The twisted ribbons of sagne incannulate and the “little hats”, cappelletti (below), turn out to be topologically identical: given sufficiently pliant dough, deft hands could stretch, twist and remould one shape into the other without the intervention of a knife or pair of scissors.
Whimsical though such insights may be, the project has a serious note too. Legendre’s pasta taxonomy provides a playful proof that immense variety and seeming complexity can be reduced to simple mathematical beginnings. Legendre is convinced that could lead to a new, more efficient way of translating design into engineering that is useful for much larger structures. Plans for an arbitrarily complex skyscraper, for example, might be reduced to equations for each of its three dimensions just like those that define the pasta shapes. “You can see the equations for a cross-section as indicative of a floor, with a third equation for the elevation,” he says.
“The approach could help architects translate design into engineering”
In fact, he has already put the principle into practice. Legendre’s in Singapore has an undulating form more than a little reminiscent of graceful pasta-like curves, and was modelled using exactly the same principles. “I just gave the engineers equations,” he says.
His own pasta shape is next on the menu. His original intention there was to bridge a gap between his passion and his profession. The pasta world has a relative dearth of the sturdy, rectilinear shapes that form the basis of most architecture. In the current pasta taxonomy, this sort of form is represented only by trenne, hollow bars with a triangular cross-section. But making such seemingly basic shapes accurately turns out to be fiendishly difficult using the traditional process of extruding the dough through a bronze die – a wrinkle that Legendre is trying to iron out with a pasta manufacturer.
Do things need to be that complex? My imagination is piqued by the idea that I might one day hook my computer, equipped with a pasta modelling package, to a 3D printer and print my own pasta. Legendre is not so sure the results would tickle my taste buds. Each pasta shape is the product of a different regional or local tradition, and centuries of painstaking R&D to match the right shape with the right sauce, he says.
That’s the kind of love mathematics cannot buy – but it might, perhaps, be food for another project. “I would love to see a book that deals with the right seasoning as rigorously,” he says wistfully.
Me too: perhaps then alphabetti spaghetti and its oozing tomato sauce will be given the belated recognition it deserves. Meanwhile, I have to admit I’m regarding the melange of pasta, buffalo mozzarella, aubergines and tomatoes in front of me in a new light. Legendre, for his part, is having the risotto.
Primi piatti
The Italian designer Giorgetto Giugiaro has a string of supercars to his name, conceived for the likes of Ferrari, Maserati and Lamborghini. In 1999 he was voted “car designer of the century” by an international jury of motoring journalists.
Less well known are his activities as a designer of pasta. In 1983, the Neapolitan manufacturer Voiello commissioned him to design a new shape compatible with the traditional manufacturing method of extrusion, in which the pasta dough is forced through a slit in a bronze die. In the event, his design, consisting of two parallel tubes with a flap protruding from their join, rather landed him in hot water. While pleasing on the eye, its intricacy meant that different parts of the pasta cooked at vastly different rates.
In 1987, the celebrated designer Philippe Starck conceived a similar-looking shape for the French pasta maker Panzani. Called the , it resembled a yin-yang symbol elongated in a third dimension. It, too, failed to break through into the pasta big time.
Fun rather than practicality seemed to be on the minds of two designers from the Bezalel Academy of Arts and Design in Jerusalem, Israel, who devised their own pasta in 2009. Resembling penne, it before cooking.
- Pasta by Design by George L. Legendre (Thames & Hudson, 2011)
