Can’t say I really understand what they mean, but found these “ideal circular membranes” for tuned drums.  The black number is the ideal value, plus kettle drum (red) and tabla (blue).

Via: +plus Magazine

Some of the purposes for which models are constructed are (1) to obtain answers about what will happen in the physical world (2) to influence further experimentation or observation (3) to foster conceptual progress and understanding (4) to assist the axiomatization of the physical situation (5) to foster mathematics and the art of making mathematical models.

From “The Mathematical Experience” by Philip J. Davis and Reuben Hersh, pg. 78.

The modern mathematician finds the space of three dimensions, in which our visible universe is containled, entirely too contracted for his conceptions, and is obliged to imagine a space of “n” dimensions in order that his fancy may find room to disport itself. But it is a new idea, on the part of the novelist, to make the conceptions of transcendental geometry the basis for an amusing story.

The very short article goes on to compare “Flatland” with “Through the Looking Glass” and their use of geometry as speculative and imaginative.

In trying to find more about this term, it appears that sadly the intelligent design crowd has laid claim to it.  The most I could find (in an admittedly short search) was this related Wikipedia article on “Complex Geometry“:

In mathematics, complex geometry is the study of complex manifolds and functions of many complex variables. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric chapters of complex analysis.

Some images from the interesting (if not redundantly titled) Mathematica “Graphics Gallery of Mathematical Art Images“.  Great names on these too.  The above image is titled “Colored Brillouin Zones of a 2D Square Lattice” by Michael Trott.  Again, I would love to title pieces as scientists do.  A few more after the break.

“The Code 1635 3-color Totalistic Cellular Automaton” (no attribution)

“Infinite Windings” (no attribution)

“Equicontour Surface of a Random Function” also by Michael Trott

An extremely deep dive into the mandelbrot zoom. If the final frame were the size of your screen, the full set would be larger than the known universe.

Via: Chemistry and Complexity (by way of the Make blog)

Random Geographic Coordinates – plan a vacation this way?

Random Bitmap Generator – not that this is that hard to do with simple programming, but a nice and simple interface for those not inclined