Phi appears in a number of geometric constructions using circles. There are a number of geometric constructions using a circle which produce phi relationships, as described below. Among mathematicians, there's a bit of a competition to see how few lines can be used to create a phi proportion, or golden section, in the construction, or how many golden sections can be created … [Read more...]
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.
Bucky balls are based on sixty coordinates all based on phi. Bucky balls are named after Buckminster Fuller, who popularized the geodesic dome. The shape defined by Bucky balls is also found in the Carbon 60 molecule, a form of pure carbon with 60 atoms in a nearly spherical configuration, the truncated icosahedron and soccer balls. Bucky balls consist of 60 points on the … [Read more...]