# Very Minkowski

Geometry Level 5

Consider the Euclidean plane equipped with the rectilinear metric. In this metric, the distance between two points $$(a,b), (x,y)$$ is defined as

$d((a,b), (x,y)) = |x-a| + |y-b|.$

We call the resulting geometry as Minkowski geometry. For example, in Minkowski geometry, the points $$(1,5)$$ and $$(3,2)$$ are $$|3-1| + |2-5| = 2+3 = 5$$ units apart.

Recall that a circle is given by a point $$x$$ and a radius $$r$$; a circle is the set of points that have distance exactly $$r$$ from $$x$$.

Consider a circle in Minkowski geometry. It can be proven that the ratio of its circumference to its diameter is constant. Find this ratio.

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