Circles to Rectangles - Tortilla Wraps

Sometimes, algebra and geometry apply to food.

The problem I wanted to solve was how to make a wrap with a single large (10") flour tortilla. Being a perfectionist, I wanted a rectangular tortilla so that the amount of bread was reasonably even through the length of the wrap. With a round tortilla, the ends don't quite enclose the food while the center becomes rather chewy with all the tortilla layers. Knowing that moistening a tortilla and pressing it together will make it adhere, I decided to figure out how to cut a circular tortilla, rearrange the pieces, and wind up with a rectangular tortilla. The strategy I chose was to cut pieces to create corners which could fill the vacant corners.

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But where should I make the cuts in the tortilla?

From the diagram, we can describe a few constraints on the lengths and angles.

  1. a + b = r
  2. r * sin(o) = b
  3. r * cos(o) + a = r

Solving the last equation for a yields a = r - r * cos(o). Substituting that and the second equation into the first equation gives r - r * cos(o) + r * sin(o) = r.

Simplifying: 

r - r * cos(o) + r * sin(o) = r
-r * cos(o) + r * sin(o) = 0
-cos(o) + sin(o) = 0
sin(o) = cos(o)

And for the sine and cosine to be equal, o must be 45 degrees.

Now that we know the angle, we can apply this pattern to a tortilla by eye-balling where we would cut the tortilla if we were to turn it into quarters. Once we have the points around the edge of the tortilla, we can cut opposite chords, then cut those parts into symmetric halves.

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Now that the pieces are arranged, wet them and press them into place with the heel of your hand.

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And now we have a rectangular tortilla. Time to add the meat (evenly!)

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and veggies

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and cheese

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and dressing

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and a dash of fresh ground red and black pepper.

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Wet the upper portion of the tortilla

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and firmly roll the wrap.

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Cut it in half so it can fit in a sandwich bag.

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These taste pretty good, if I do say so myself.

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And that's how you apply geometry and algebra to get food fit for a perfectionist!

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