Everyone loves $pi$. It’s usually the first irrational number someone encounters. $pi$ is conceptually simple enough that it can be explained with basic geometry. A circle with diameter 1 has a circumference of $pi$. $pi$ is the ratio between the circumference and the diameter. But why does $pi$ have to have that value? Could it have some other value? The answer is yes! Circle is the collection of all points that are an equal distance from the center. Not all constant-cost functions will create the same shape. Mathematicians have discovered various metrics that can be used as distances, such as Manhattan distance and maximal distance. The value of $pi$ can be different for each metric. P-norms are a generalization of these metrics, with Euclidean distance, Manhattan distance, and maximal distance being specific examples of p-norms. Different values of $p$ in the p-norm formula yield different metrics. In all other metrics besides the p-norms, $pi$ is proven to be between 3 and 4. Lastly, a hexagon metric yields a value of $pi$ equal to 3. So, in addition to celebrating $pi$-day on March 14th
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