What artists have used geometry to great advantage in their work?

Answer 1

One problem with geometry, is that most people learn Euclidean geometry. It is intuitive but his parallel postulate creates great problems for mathematicians. It can neither be proved or disproved. There are consistent geometries if you accept that postulate, but there are equally consistent geometries for the two possible negations (no parallel lines and many). Artists are not necessarily constrained by geometric "realities" or restrictions. And many have either used geometry or ignored it to great effect.

For example, many renaissance artists used projective geometry and the idea of a vanishing point in their art. This gave their work a better 3-d perspective than earlier works which often looked flat. Images in the background used to be unrealistically large and so on.

In the 20th century, artists like MC Escher played on geometry, perspective, tessellation (tiling).

Finally, many cubists chose not to use "normal" geometry, but chose to simultaneously portray things from several perspectives at the same time.