Instead of trying to tile a continuous plane, consider a two-dimensional ... this emerging sort of principle that higher-dimensional geometry is just nasty,” Tao said. “That pathologies ...

Several years ago Menkes van den Briel, an industrial engineer at Arizona State University, tackled a "nonlinear assignment problem with quadratic and cubic terms in the objective function." In ...

in the same manner that Practical Geometry, that is to say, the intelligent use of drawing and of graphical methods, deals with plane geometry. If, in solid geometry, we concerned ourselves only ...

In hyperbolic geometry the plane is not necessarily so flat. Yet while nature has been playing with hyperbolic forms for hundreds of millions of years, mathematicians spent hundreds of years ...

This is a layer of spheres packed hexagonally, like our optimal packing of circles in the plane. Similarly, you can stack a second layer on top of this one, nestling it in the gaps between the spheres ...

Aschauer said he plans to use the geometry as a guide to dead ends and promising but unexplored corners in the landscape of possible patterns. And using the mathematical language of the symbolic plane ...