This example demonstrates how to convert between geographic coordinates, Mercator projections, and map tile coordinates in Ruby. It defines a module with functions for transforming latitude/longitude pairs to and from Mercator-projected coordinates, as well as scaling those coordinates to specific zoom levels. The code also includes utility methods for calculating an optimal zoom level and center point that fits a set of locations within a given viewport, optionally accounting for padding. The implementation relies on the Ruby Math library for trigonometric and logarithmic operations, with no external dependencies.