Pizza algebra

Recently I have seen several discussions on the internet about the ratio of the diameter of a pizza offset more than a smaller one, and arguments against the effect of the size not only apply to the filling (or topping, depending on how you see a pizza), but also the amount of edge it has (which many fresh people don’t eat).

The quickest way to solve this problem is to determine a formula from the radius (or diameter), edge width and price variables.

Radius = r;
Border width = b;

Thus, the filling of the pizza will be given by the expression:

π. (r-b) ²

To improve our analysis, we will take a menu of any pizza that has announced its diameters.

Image obtained at https://www.ezimonteiro.com.br/review-pizzaria-fragata-porto-alegre/

In this distribution, we have:
Medium Pizzas: 30 cm in diameter;
Large Pizzas: 35 cm in diameter;
Family Pizzas: 42cm in diameter.

The amount of fear in each of them will be:
Medium Pizzas: π. (15-b) ²
Large Pizzas: π. (17.5-b) ²
Family Pizzas: π. (21-b) ²

See that we kept the size of the border as undefined, because we don’t want to reach such a “silly” result. Let’s first analyze the proportion of your filling (or topping) by price, ignoring the option of large pizza with 3 or 4 flavors.

Medium Pizzas: π. (15-b) ² / 29.90
Large Pizzas: π. (17.5-b) ² / 34.90
Family Pizzas: π. (21-b) ² / 52.90

Assuming then a variation in the width of the pizza’s edge between 0 and 50mm (assuming a pizza with more than 50mm in width is already heavy enough for this blog), we can observe how the cost benefit of the pizzas varies, that is, the amount of filling (in area) divided by the price of the pizza.

We subtly see that Pizza Grande will only have a better cost benefit than Pizza Família, in case we assume a pizza without a border (or if you consider the border as tasty as the filling). In other cases, the curves move apart, making the family-sized pizza more and more cost-effective compared to other pizzas.

This reasoning remains analogous to other menus, simply replacing the spokes and the prices.

I hope this helps you decide which size of pizza pays off the next time you make a pizza party.

Cover image credit to Igor Ovsyannykov from Pixabay

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