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Golden Ratio Discovered In a Quantum World
FiReaNGeL writes "Scientists have for the first time observed a nanoscale symmetry hidden in solid state matter. 'In order to study these nanoscale quantum effects, the researchers have focused on the magnetic material cobalt niobate. It consists of linked magnetic atoms, which form chains just like a very thin bar magnet, but only one atom wide.' By artificially introducing more quantum uncertainty, the researchers observed that the chain acts like a nanoscale guitar string. The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618, which is the golden ratio famous from art and architecture. The observed resonant states in cobalt niobate are a dramatic laboratory illustration of the way in which mathematical theories developed for particle physics may find application in nanoscale science and ultimately in future technology."
You're ALL irrational.
This really is interesting, though. The Fibonacci sequence shows up all the time in nature, but this is, to my knowledge, the first time in a non-biological function.
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Here's my cut at a car analogy. Notice that a naturally recurring form-factor for popular cars involves a height to length ratio of 1:1.618. That ratio shows up again in that "rise to run" ratio of windshield rake. ...and again in overdrive gear ratio... and yet again in...
The golden ratio phi is "the most irrational number", in some sense. If you try to take better and better rational approximations to phi, obviously you need to go to bigger and bigger denominators in the fraction. In the limit as the error tolerance goes to zero, the necessary size of the denominator grows at a certain asymptotic rate. One can show that for phi this rate is the largest possible, so the golden ratio is the hardest number to rationally approximate.