## Computerized Math, Formal Proofs and Alternative Logic

Using computer systems for doing mathematical proofs - "With the proliferation of computer-assisted proofs that are all but impossible to check by hand, Hales thinks computers must become the judge."
posted by kliuless on Mar 16, 2013 - 25 comments

## Impossible Crystals

"This is a story of how the impossible became possible. How, for centuries, scientists were absolutely sure that solids (as well as decorative patterns like tiling and quilts) could only have certain symmetries - such as square, hexagonal and triangular - and that most symmetries, including five-fold symmetry in the plane and icosahedral symmetry in three dimensions (the symmetry of a soccer ball), were strictly forbidden. Then, about twenty years ago, a new kind of pattern, known as a "quasicrystal," was envisaged that shatters the symmetry restrictions and allows for an infinite number of new patterns and structures that had never been seen before, suggesting a whole new class of materials...."

Physicist Paul J. Steinhardt delivers a fascinating lecture (WMV) on tilings and quasicrystals. However, it turns out science was beaten to the punch: a recent paper (PDF) suggests Islamic architecture developed similar tilings centuries earlier.
posted by parudox on Mar 18, 2007 - 11 comments

## The so-called Golden Ratio

A good article on the so-called Golden Ratio.
posted by stbalbach on Jun 13, 2004 - 19 comments

## It all started with rabbits

Fun with Fibonacci numbers. So you say you scored 130 on yesterday's IQ test, did ya?
posted by archimago on Oct 28, 2003 - 5 comments

## The golden section

The golden section (math, graphics) is an important relation used by artists and mathematicians, among others. I'm curious if any of you have good examples of recent use.
posted by lbergstr on Apr 15, 2002 - 45 comments

## "Self-similar syncopations: Fibonacci, L-systems, limericks and ragtime"

"Self-similar syncopations: Fibonacci, L-systems, limericks and ragtime" Along the lines of the book "Godel, Escher and Bach", an award winning essay looks at the mathmatical roots of popular music. I think I'm going to have to find a way to analyze some of my fave mp3's to see how they fall into the Fibonacci sequence...
posted by katchomko on May 19, 2000 - 2 comments

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