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Square Box, Round Pizza, Triangle Slices
Demystifying Pizza Geometry
One year ago today, while sitting in Giovanni’s pizza shop in Commack, NY, and enjoying a slice, the below sign on the wall caught my attention:
I thought to myself:
A circle has one side,
A triangle — three,
What shape is two-sided?
A square it can’t be!
In this cozy pizzeria setting, it turns out, there are geometrical shapes with 1, 3, and 4 sides, but none with 2. The sign was right. I’m confused.
In circles, triangles, and squares, the shape-defining line begins at a point and returns to that point, never crossing itself. A line with two ends doesn’t close back on itself … unless it follows the surface of the Earth all the way around until it does. But then it isn’t a line anymore, but a circle or an ellipse when looked at from the side. Despite the two-ended line being excluded from the trio of shapes, its contribution to the geometric wonders observed in round pizza should not be diminished. Without the line, there would be no triangles, and hence, no slices.
The line’s contribution in the case of pizza, however, is very deceiving. As the line gets applied more, the number of triangles increases, which at first increases the line’s sense of self-worth. What the line initially doesn’t realize is it is working within the confines of a circle, which in turn is confined by a square (box). Yes, the number of slices increases as more lines are cut through the pizza, but the size of the pizza stays the same.
Not to be stifled by a square, the line quickly figures out that by applying itself just four times to the circle contained within the box, it will have already covered a distance equal that covered by the box’s four sides. Upon arriving at this realization, the line rests, knowing its work is complete. It signals to the circular cutter responsible for creating lines that it too can lie down and take a break.
How fortunate for the world to have round pizzas, for without them, this story…
