From Mediants to Lorentz Transformations

A pedagogical journey through the Farey diagram: rational mediants → SL(2,ℤ) matrices → cross-ratios → homogeneous coordinates → hyperbolic geometry → special relativity
Hyperbola Model (x² - y² = 1)
Classical Circular Farey Diagram
Hover over a point to see its Pythagorean triple and relativistic velocity