phi – the golden ratio

Phi (the Golden Ratio) appears in a number of very interesting geometric constructions. It appears in basic constructions of triangles and squares within a circle, the pentagon. It also defines every point in 3D space in classic solids such as the dodecahedron, icosahedron and Bucky Ball. Johannes Kepler, who first discovered the beautiful elliptical nature of the orbits of the planets in our solar system described it as “a precious jewel” of geometry.