Rectangles or Triangles: Settling the Sandwich Debate

  sandwich cutting diagrams via


A sandwich is two slices of bread enclosing a filling.
In theory. Most of us treat those bread slices as a blank canvas on which to paint the colors and contours of our appetites, our pantries, and our histories.
Mortadella or tuna? Lettuce or sprouts? White or rye? There are infinite combinations and permutations of taste and texture, each requiring its own tough choices.
But there’s one no-brainer: the cut.

I don’t mean to suggest that the decision is trivial. Quite the opposite. It’s easy because it’s an unwavering, discrete choice that most sandwich-makers settle on in childhood and seldom vary throughout a lifetime (excepting the club sandwich four-triangle imperative, but that mandate takes the decision out of our hands). Vertical or diagonal: it’s easy but never trivial; in fact many individuals believe that the success of the entire sandwich-making endeavor hinges on the choice.

According the Hellmann’s Mayonnaise State of the Sandwich Survey, a full three-quarters of Americans take a knife to a completed sandwich, with 60% making a diagonal cut and 38% slicing on the vertical. There are regional differences. A third of all midwesterners prefer uncut sandwiches, and they are more likely to finish the crusts (73% versus 63% for everyone else).

Hunch, the online recommendation engine much-loved by advertisers, includes a sandwich-cutting question in its data collection, suggesting it believes that these preferences belong in the Hunch algorithm as a signifier of other traits and behaviors. With responses numbering in the tens of millions, Hunch has ascertained that those who cut their sandwiches diagonally are partial to Ray-Ban sunglasses.

Many light eaters advocate for the four-triangle cut.
Assuming that they might not finish the entire sandwich, they like the option of working their way from point to crust. It gives them four chances with a long stretch of crust-free bread and the best access to the sandwich’s midpoint, which is likely to have the greatest concentration of sandwich filling. In this way, not unlike most pizza eaters, they can maximize the meal’s outcome (flavors and proteins) while appetites are fresh, and abandon the skimpily-filled crust ends as they fill up.

The mathematically inclined—teachers, engineers, architects, and the like—also tend to be strong proponents of the diagonal cut.
They argue that while a sandwich’s crust is constant, diagonal cutting increases the ratio of uncrusted to crusted surfaces, thereby increasing your enjoyment. It just takes a little Euclidean geometry.

bisect sandwich.bmpConsider a sandwich made from bread that’s roughly a square with 4 inch sides. That’s 16 inches of crust.
Cut it in half and you have 8 uncrusted inches of sandwich. Halve it again orthogonally and you get 16 uncrusted inches to the same 16 inches of crust.

diagonal sandwich.bmp
Let’s take that same sandwich with its 16 inches of crust, but this time we’ll cut it in half diagonally. Each long, hypotenuse side of the two triangles is going to measure about 5½ inches (who could forget Pythagoras’ theorem?) for a total of 11 uncrusted inches. Halve it again and the uncrusted edges of the four triangles add up to a whopping 22 inches to that same, original 16 inches of crust.

The diagonal cut squeezes 6 more uncrusted inches out of a single 4-inch square sandwich.
I’d say we have our winner.
The great sandwich debate of rectangles vs. triangles is finally settled. What a relief.

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