Pasta
by Design

In a London architecture office, late at night, two people are eating pasta. There's Chianti on the table — whether good or bad is unknown. George Legendre and his colleague Marco Guarnieri are looking at the same parametric equations they use during the day to define building facades. One of them says: “We're already doing this. For buildings. Why not for pasta?”

The book came out of that question. Thames & Hudson published it in 2011; it was translated into German the following year. The title is plain: Pasta by Design.

But what's inside is anything but plain.

Open the book and there are no recipes. None at all. Instead: photograph, equation, wireframe drawing, brief description. The same format repeated for each pasta shape, 92 times.

Each pasta page carries: what the shape is, where it's eaten, which sauce might work — but these are supplementary. The main subject is mathematical structure. Each shape is defined by three parametric equations using only two trigonometric functions: sine and cosine.

From fusilli to cappelletti, from spaghetti to pappardelle — the same mathematical skeleton underlies them all. Legendre's claim: there is a geometric logic connecting all pasta shapes, and that logic can be written as a formula.

Legendre borrowed a tool from biology to classify pasta shapes: phylogenetics. This is a method that maps morphological kinship relationships — similarities in form, structure, and origin — among living species. Normally used to measure the structural distance between whales and cows. Legendre used it to measure the geometric distance between rigatoni and penne.

The result: the family tree diagram at the front of the book. 92 pasta shapes arranged on a tree according to their geometric properties — edge type, surface texture, cross-section shape, folding method. It shows that two pasta shapes that look entirely different may actually belong to the same mathematical class.

Each pasta shape is defined by three equations: Π (Pi), Θ (Theta), and K, corresponding to the x, y, and z coordinates respectively. Parameters i and j take values over specific ranges; inside the equations you see only sin and cos.

Mathematically, this is parametric surface modelling. Architects use it to design building facades. Legendre applied the same system to his dinner. The geometry escapes the kitchen in other ways too — a Pringle chip is a hyperbolic paraboloid, shaped that way for the same structural reasons that keep thin-shell roofs standing.

i = 0…40  j = 0…120

Π = (0.1+sin(3i/160·π))·cos(2.3j/120·π)
Θ = (0.1+sin(3i/160·π))·sin(2.3j/120·π)
K = 0.1+j/400+(0.3−0.231·i/40)·cos(i/20·π)

i = 0…70  j = 0…150

Π = (3+2·cos(i/35·π)+0.1·cos(2i/7·π))·cos(j/30·π)
Θ = (3+2·cos(i/35·π)+0.1·cos(2i/7·π))·sin(j/30·π)
K = 3+2·sin(i/35·π)+0.1·sin(2i/7·π)+j/6

“Seeing mathematics in fusilli makes perfect sense today. Programmers talk about beautiful code, and designers use math to create organic shapes.”

— Paola Antonelli, MoMA Curator of Design & Architecture (foreword)

There is also this: Italian nonnas who have been making pasta for centuries already knew — without calculation — all the geometry Legendre spent years computing in a London office. Knowledge that lived in their hands, he formalised into symbols.

Is that an injustice? Perhaps. But it is also one of the oldest problems in the history of mathematics: the conversion of intuitive knowledge into symbolic knowledge. Turning a point into a line, a line into an equation. In a way, Legendre paid the nonnas a compliment — he found their shapes so beautiful he wanted to make them permanent. Henry Billingsley had the same instinct in 1570 — his English Euclid came with paper fold-out solids you could hold in your hand.

Selected shapes from Legendre's catalogue, mapped by category, geometric profile, regional origin, and canonical sauce pairing.

No one and everyone. The honest answer: if you're looking for recipes, you're at the wrong shelf. If you want to understand how pasta engineering works, why some shapes hold sauce and why others don't — the book explains those too, but as footnotes.

The real audience sits at the intersection of any of these: mathematicians, architects, designers, data visualisation practitioners, Montessori teachers, and pasta enthusiasts who don't mind being a little peculiar — the same breed that finds a shelf built on the Fibonacci sequence perfectly reasonable as furniture.

One Amazon reviewer loaded the equations into Mathematica and started spinning the 3D shapes on screen — children who saw it all said “let me try that!” That is one of the finest things a book can achieve.