The Unreasonable Beauty of Mathematics [Slide Show]
Mathematical structures both natural and man-made dazzle the eye
![The Unreasonable Beauty of Mathematics [Slide Show]](https://www.scientificamerican.com/sciam/cache/file/05A502EE-A2A7-4148-AACCA472943E4EF2.jpg?w=590&h=393)
The Unreasonable Beauty of Mathematics [Slide Show]
- KNOT THEORY: The trefoil is the simplest knot in mathematicians' classification. Knot theory goes back to the 19th century, when physicists briefly thought knots might explain atoms; mathematicians continued to develop the theory for its inherent interest. Lately the theory has found use after all. It comes up in quantum field theory, which describes the fundamental particles and interactions, as well as proposed quantum theories of gravity such as string theory and loop gravity. Robert G. Scharein
- MÖBIUS PROTEIN: The major component of high-density lipoprotein (HDL, sometimes known as "good cholesterol"), apolipoprotein A-I, consists of a kinked helix about 12.5 nanometers in its longest dimension. Mike Tyka of the University of Washington, a protein-folding expert and artist/tinkerer, maintains a catalog of his favorite molecules. Mike Tyka, University of Washington. Image was rendered using PyMol
- HEAVENLY SPIRALS: Spiral patterns occur throughout nature, perhaps most dramatically in spiral galaxies. This pair of galaxies has particularly unusual spiral patterns that are presumably the result of the gravitational tidal forces between them. The inner spiral arms of the upper galaxy (UGC 1810) are not planar, and the outer arm may have been pulled into a ring by a direct collision with the lower one (UGC 1813). NASA, ESA, and the Hubble Heritage Team (STScI/AURA)
- DOUBLE SPIRAL: Paul Nylander maintains an incredible collection of mathematical art, along with the Mathematica code to recreate it. Paul Nylander
- FRACTAL BROCCOLI: John Ostrowick, responding to our Twitter call for examples of natural mathematical beauty, suggested Romanesco broccoli. This photo by Jon Sullivan was selected by Wikipedia users as one of the most spectacular on that site. Jon Sullivan
- FRACTAL BUBBLES: Richard Taylor specializes in discovering the occurrence of fractals in the world. (He has argued that fractal geometry can tell a real Jackson Pollack painting from a knock-off.) He took this picture at the edge of the pond in Sydney, Australia. The bubble outlines have a fractal dimension of 1.3, which people tend to find the most aesthetically pleasing. Taylor argues that our eyes scan a scene using a fractal pattern with a similar dimension. Richard Taylor, University of Oregon
- FAMOUS FRACTAL: This is a version of one of the best known fractals, the Julia set. Fractals in general are a compelling example of how abstract mathematical forms, generated by seemingly simple algorithms in which a pattern repeats on multiple scales, are capable of intricate beauty. Nature is full of such patterns. Tom Beddard
