We start by studying the geometry behind the Egyptian pyramids . The golden ratio and the Platonic solids were important in Greek culture. The main Roman contribution in this area were the books of Vitruvius . Next comes the Renaissance and the origin of perspective and projective geometry. We will also look at the work of D rer and da Vinci .
Ornamental patterns are important in all cultures.
Among the most famous are the Islamic patterns at Alhambra. This brings in symmetry groups and crystallography. The work of Escher is rich in mathematical content. Much of it is related to hyperbolic geometry. Another beautiful application of geometry is kaleidoscopes .