http://www.newscientist.com/article/mg21228342.400-spaghetti-functions-the-mathematics-of-pasta-shapes.html
* 12 October 2011 by [33]Richard Webb
[33] http://www.newscientist.com/search?rbauthors=Richard+Webb
What possessed an architect to boil down the beauty of pasta to a
few bare formulae?
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 New Scientist, 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.
According to a [36]recent survey 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 [37]the
league 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.
[36] http://www.bbc.co.uk/news/magazine-13760559
[37]
http://www.internationalpasta.org/index.php?cat=22&item=7&lang=2&item_child=2
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.
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 [38](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 [39]crocheted
representation of a hyperbolic plane that adorns my desk at New
Scientist, 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.
[39] http://www.math.cornell.edu/~dwh/papers/crochet/crochet.PDF
Sharp inflections, such as the undulating crests of the
cockscomb-like galletti (shown on page 48), 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.
In fact, he has already put the principle into practice. Legendre's
[40]Henderson Waves bridge 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.
[40]
http://www.nparks.gov.sg/cms/docs/southern_ridges/SR_Henderson_Waves.pdf
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.
Bibliography
1. Pasta by Design by George L. Legendre (Thames & Hudson, 2011)
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 [41]"Marille" 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.
[41]
http://jalopnik.com/5594815/this-pasta-was-designed-by-the-man-who-designed-the-delorean
In 1987, the celebrated designer Philippe Starck conceived a
similar-looking shape for the French pasta maker Panzani. Called the
[42]Mandala, it resembled a yin-yang symbol elongated in a third
dimension. It, too, failed to break through into the pasta big time.
[42]
http://www.tribu-design.com/collections/index.php?ac=f&pict=1&lg=en&ty=35&st=4
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
[43]could be used as a whistle before cooking.
[43]
http://www.skyscraperlife.com/bar-beret/21524-design-pasta-fischio-whistle-paste.html
Richard Webb is a feature editor for New Scientist
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