The first review was under the spell of Sacred geometry" where statements like "everything traces back to radius and arc" illustrated some review topics. This clip alone illustrates the silliness of absolute statements which have influenced religious approaches to mathematics since the times of the Pythagreans. Even after 2500 years, can find Pythagorean fallacies mirrored in modern sacred geometry. Start at about 4 minutes into this movie, where platonic solids are placed into the Metatron cube (an icon in sacred geometry). Things work well for the tetrahedron, cube and octahedron but fail for the dodecahedron and icosahedron. The artist is forced to "replicate" the metatron to reach the continuum. This platonic solid story also reminds of Kepler's Hamonices Mundi, where the metaphysical music of spheres appeared with the goal to explain the motion of planets using platonic solids. The stubbornness to stick to simplistic concepts like "radius and arc" was a major stumbling block to describe planetary motion correctly and getting away from a geocentric model, where circles or epicycles = circles on circles were used to describe planetary motion. Geometry has influenced religions since ancient times. It is still used for meditative purposes. |
Charles Gilchrist is an artist, who makes beautiful pictures which are influenced by simple geometry. The clip is from here. The clip was used in the first midterm review to illustrate polar coordinates. |