Pure mathematicians are completely conversant with the creative nature of their research. In fact, we refer to the Art of Mathematics. From out of nothing, almost, come ideas that, when fully developed, lead to wondrous new mathematical discoveries that time and time again subsequently find application in the real world.
Mathematics and Art are also closely connected. For example, think of perspective. Geometers and artists developed the ideas, and the latter put them to use in their paintings (see the work of the Venetian artist Canaletto for example).
I trained as a mathematician, but have also had a life long interest in painting, visiting galleries in many parts of the world. Particularly appealing to me are the painters who, like Canaletto or the Flemish/Dutch painters of the 17th Century (Vermeer for example) use perspective.
Into more modern times, Albrecht Escher made wonderful use of the new discoveries in geometry (elliptical and hyperbolic geometries being prime examples – triangles always have more than 180 degrees in the former, which means that parallel lines always meet, or triangles always have less than 180 degree is the latter, in which case parallel lines diverge).
There are many Escher drawings with which you may be familiar. Here’s one:
One of my favourites, because it has its genesis in hyperbolic geometry, is:
Imagine my joy when I stumbled on a web site which enables one to create similar designs, but using one’s own images. Here’s an example. I started with the image below (how I made it is explained in the previous post):
I then passed it through the Hyperbolic Tiling routine to get:
With a little further trickery, I then produced this:
I think that’s pretty neat.
And there are many more mathematical transformations which can be output as images on the website.
OK, that’s it. I am off to play some more.