# The Geometry and Topology of Pasta

I’ve always had a geeky appreciation – and awe – of mathematics. I have spent countless hours tinkering with programs that create math-based designs like fractals and Spirograph-style curves. As a young teenager I spent hours playing with an oscilloscope making sound waves dance on the tiny screen. But I never really thought much about the math behind pasta until I stumbled on two books: The Geometry of Pasta and Pasta by Design. And once you open them, you have one of those ‘ah ha!’ moments where you discover mathematics and cooking intersect.

These books offer radically different approaches to pasta from my usual reading (and neither are about making your own pasta, although the shapes and histories may help inspire you). What is odd is that both take an unusual approach and yet both were published within a year of one another.

Shape of course matters. The shape of pasta defines several key elements: amount of surface area and size (which matters to cooking and when determining which utensils to use to eat it), thickness (matters to cooking time), sauce holding ability (rough or convoluted shapes hold more when eating) and visual appeal. Shape determines how much water a piece of pasta absorbs, how the heat is absorbed and transferred – knowing these data, one could choose the type of pasta to best match a particular sauce, or vice versa.

Texture, too matters, to sauce retention, cooking and mouth feel, but that’s micro-topology, and not covered here.

The first, The Geometry of Pasta, is really a cookbook designed to both entertain and express the complex design inherent in pasta shapes, as well as offering a bit of history and regional information. It comes from the chef of a very chic UK restaurant ( Bocca di Lupo) and a brilliant graphic designer. It also sports a delightful website in which you can explore the shapes of 77 types of pasta in elegant black-and-white illustrations:

The text that accompanies that illustration of lasagna ricce at the top – the shape for which I recently acquired an attachment cutter for my Atlas pasta machine – says:

Lasagne ricce are crimped, wavy or ruffled lasagne – lasagne with wavy edges – that are decorative and may allow lighter sauces to infiltrate the dish better. This shape of pasta is primarily a southern thing. Across Sicily, baked al forno with layers of a rich ragù and ricotta, it is a staple of the Christmas table.

Under the heading of sauces, there is a recipe for using lasagna ricce which, since it contains mammal meat, I will have to eschew. However, there are other equally attractive recipes on the site (and in the book) I can substitute. If, that is, the authors don’t know I’ve done so. They have written in the introduction, that…

…the Italian “preoccupation with choosing the right pasta shape to go with the right sauce” is not just some silly European thang, but can actually “[make] the difference between pasta dishes that are merely ordinary and truly sublime”.

Reviewer Joanne at Eats Well With Others has written:

Using the geometry of a given pasta – each with its own nuances, personality traits, online dating profile – one can actually turn the art of pasta preparation into a science; an architectural study, if you will.

If every pasta shape requires its own unique sauce, I’m doomed. I’ve mixed and matched my way into some Dantean circle of Hell where only wayward pasta makers end up…

I don’t see it that way, however – rather I see the shape of the pasta should fit more the mood of the meal and the diners. A lasagna with a rich tomato sauce for me is more relaxed and wintry than a ravioli in a cream sauce, although I will concede a farfelle might need more attention to its sauce than a spaghetti. Plus, not eating mammal, the authors’ philosophy would severely limit my choices.

I’m more fortunate in their recipe for penne all ‘arrabbiatta, which is a favourite, spicy dish and is presented as a tomato dish (locally you can find it with either meat or chicken as well).

Caz Hildebrand, the graphic designer, and Chef Jacob Kenedy found more than 1,200 names for pasta while researching their book, according to an interview they gave on NPR. That doesn’t mean every name is for a different shape – regional names may apply to similar shapes – but it shows how daunting it can be to be thorough in a book about pasta. (Food-info.net lists 103 different types, Pasta Fits has 53, and Wikipedia lists around 130.  In her book, The Pasta Bible, Jeni Wright has photographs of 172 types, albeit some are simply colour variations).

The second book, Pasta by Design, is really about the math: the curves, the angles, the topology 0f 92 types of pasta, each illustrated with an equation, a 3D image and a photograph:

It’s not a cookbook, but rather a mathematical and architectural way to express the complexity, delight and sometimes whimsy of a popular food through a different medium other than cooking. It also includes a novel taxonomy for pasta. The Wall Street Journal reviewed it, noting,

The shape of each is described in elaborate mathematical formulas and shown in a technical illustration. There’s also a pasta family tree that groups the shapes into categories, like solid or hollow, smooth or striated, twisted or bunched.

Reviewer Ryan King called this book the…

…biggest visual and detailed collection of pasta shapes ever published, a triumph of design, mathematics and a project that’s led to some interesting discoveries.

And reviewer Maria Popova wrote:

Taking a cue from the science of phylogeny—the study of relatedness between groups of forms in nature—Legendre distills the astounding variety of pasta types and the often confusing nomenclature of their classification in an obsessive family tree based on their morphological features. Each shape is described in a meticulous mathematical formula, coupled with a minimalist yet expressive photograph and a short paragraph of cooking suggestions for the respective pasta variety.

Co-author and architect, George Legendre, told Macleans magazine his book was “the first visual dictionary of pasta,” to be used as an inventory, guide and culinary resource. He added he felt there was a practical side to the book: “..I know it’s the strangest aspect, but I never saw mathematics as the point of the book. I wanted to help people buy pasta.”

This new, technical approach to pasta has spawned some fascinating commentary on other sites. It seems to have begun a few years back when Dutch PhD student, Sander Huisman, wrote mathematical models to recreate some pasta shapes. He noted:

Take gemelli, for example, spiral pasta. I started with a lemniscate, the mathematical symbol for infinity. Then I chopped a piece off, pulled it out and twisted it around. I think it took me an hour and a half to get the 15 formulas.

Mathematical blogger Steve Kass posted this image of a simulated conchiglie rigati:

and then this formula for the shape:

While I can’t profess to translate the math in the formula, I do appreciate that it defines in concise form the complex curve of the piece as it widens and narrows, along the X and Y axes. And the formula, even to the uninitiated like myself, simply looks beautiful by itself. So crisp, so symmetrical. He also shares the equation for a different shape, cavatappi, on a separate post.

Even if you lack the requisite mathematical education to fully appreciate the equations, the beauty of both books is striking, and the approach make you think about pasta in an entirely unexpected and delightful way.

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