Pi

Circumference of the circle divided by twice the radius...

Suppose we discretized the plane and we want to compute lengths of curves based on their approximations by digital curves.

Observation: The perimeters of a square and the inscribed circle are the same:

Indeed, it takes exactly as many vertical (and horizontal) steps to get from the left end of the circle to the top - no matter whether you make just one turn or many.

Therefore, $\pi=4$!

As the image below suggests, the discretization of the plane makes it curved...

Two-dimensional scientists of the flat and curved “surface worlds” check the Euclidean theorem about the sum of the angles in a triangle. From G. Gamow, One, Two, Three... Infinity.

Specifically, sphere-like (positive curvature).