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ROBERT SMITH, host:

We're all back with ALL THINGS CONSIDERED from NPR News. I'm Robert Smith.

This is the weekend of the turkey sandwich. And with that masterpiece of leftovers comes a crucial decision - do you cut the bread straight across into rectangles or corner to corner into triangles?

Okay. So, maybe you haven't given this choice a moment's thought, but our producer, Alice Winkler has - a lot of thought.

ALICE WINKLER: I am not alone. I always thought the diagonal cut just made the sandwich better, and then I started to ask around and it turns out, most everyone I asked agreed - even my kids.

Unidentified Child #1: Diagonal.

WINKLER: Really? How come?

Unidentified Child #1: Because it tastes better that way.

Unidentified Child #2: Because it gets less crust because you're cutting it that way in half.

WINKLER: But, okay, they are my kids and it could be genetic. Kemp Minifie, however, was the executive food editor for Gourmet magazine, until its recent demise, and she agrees: diagonal rules.

Ms. KEMP MINIFIE (Former Executive Food Editor, Gourmet Magazine): Well, right angles can be boring. We think of rooms. We like curved windows, bay windows. And I think in our life, there's always that little bit of out of the box. I'm not going to be boxed in.

WINKLER: Words to live by for sure. Minifie says the diagonal cut creates the illusion that your sandwich is bigger. If you like to start with a corner bite, it's easier to fit that sharp angle into your mouth without a mess. And if you like to avoid crust, you have a nice, wide soft surface to attack. Her passion was born early.

Ms. MINIFIE: My mother used to cut her sandwiches in half crosswise and I never liked that. I've always liked the diagonal and the diagonal is what you've got in the deli and a coffee shop or diner. And I used to love to watch them make it, let's say the grilled cheese. So, they have it on the griddle and then they'd slide it off, and with that one swift stroke cut it in half diagonally.

WINKLER: I wanted to witness the magic, so I headed out to the Tastee Diner -that's Tastee with a double E at the end and a mountain of home fries biding their time on the grill. And just like out of Kemp Minifie's dream, I found Spanky(ph).

Mr. NATHAN SPANKY LEWIS(ph): If it's squared off, it doesn't even look like a sandwich, you know?

WINKLER: Nathan Spanky Lewis is an institution at this griddle in Bethesda, Maryland, and you will never catch him cutting a sandwich straight from side to side. Why? He sums it up in a word:

Mr. LEWIS: It's just reputation in 30 years of cooking.

WINKLER: Reputation? I left the Tastee Diner full but not quite satisfied. Then it hit me: who knows more about angles and aesthetics than an architect?

Meet Kevin Harris(ph), who designs homes in Baton Rouge, Louisiana. His favorite sandwich, by the way, is a Reuben. And if he were making one at home:

Mr. KEVIN HARRIS: I would cut it on the diagonal, absolutely.

WINKLER: Kevin Harris says that since the time of the pyramids, architects have understood the supremacy of the diagonal line.

Mr. HARRIS: By cutting it on the diagonal, you have the hypotenuse of the rectangle, which is, of course, the longest section. And it exposes more of the interior of the sandwich. And by exposing the interior, it engages more of your senses before you take the first bite. It's less of a surprise and it's more revealing, almost like burlesque dancers. Covered enough to be clothed, but uncovered enough to be very, very appealing.

WINKLER: So, it comes down to sex and to math really. The amount of crust on a sandwich does not change no matter how you cut it. But the amount of surface area without crust can change. If you start with a four-inch square sandwich, for example, you end up with three inches more crust-free surface just by cutting corner to corner.

I called Paul Calter, an emeritus professor of mathematics, to check my numbers. I was right, but he was ready to talk about deeper things - the mystical force of three, the Father, the Son and the Holy Spirit, and Plato's book, "The Timaeus."

Professor PAUL CALTER (Mathematics, Vermont Technical College): He describes the creation of the universe and he wants to describe it in terms of small elements. Now, they thought that there were four elements - earth, air, fire and water - and he ascribed a solid to each of these so-called platonic solids. And Earth was represented by the cube, and the cube has square faces. And he wanted to subdivide the faces down further. So, what he did, he didn't cut the square face in half parallel to the sides, he cut it corner to corner.

So, this triangle, which is technically the isosceles right triangle, according to Plato, was one of the basic building blocks of the universe.

WINKLER: Whoa. The universe, the sandwich, the diagonal, it's all coming together.

All right. This is where I admit that maybe the search for an answer to an insignificant question has gone a little too far, so I leave you to your turkey sandwich and your knife. The choice is yours and yours alone.

SMITH: That's our producer Alice Winkler. You could weigh in on the triangle versus rectangle debate. Comment on our Web site, npr.org.

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