NSF: Science & Engineering Visualization Winners

The NSF has posted the winners to this years competition. My favourite is probably:

Möbius Transformations Revealed
Credit: Douglas N. Arnold & Jonathan Rogness, University of Minnesota, Twin Cities

Any real numbers [sic] can be plotted on a line that runs from negative to positive infinity, but throw in an imaginary component and the line becomes a plane, where complex numbers are plotted on both the real and the imaginary axes. Möbius transformations are mathematical functions that send each point on such a plane to a corresponding point somewhere else on the plane, either by rotation, translation, inversion, or dilation. It may sound confusing, but after watching this simple and elegant explanation of Möbius transformations created by Douglas N. Arnold and Jonathan Rogness of the University of Minnesota, Minneapolis, everything becomes clear. Set to classical music, the video demonstrates the transformations in two dimensions but then backs away and adds a third—placing a sphere above the plane and shining light through it. As the sphere moves and rotates above the plane, suddenly all the transformations become linked, in a way that conveys visually in minutes what would otherwise take "pages of algebraic manipulations" to explain, says Rogness.

Comments

[Jesse]

That was my favorite too.