The Hindu Business Line : The phi of rabbits, markets, hockey

While the Greek letter pi is used for denoting the ratio of the diameter of a circle to its circumference, the letter ‘phi’ is used for denoting the ratio found in a number sequence known as the Fibonacci series, write Christopher Knight and Alan Butler in ‘Civilization One’ ( www.vivagroupindia.com ).

“Leonardo Pisano Fibonacci (1170-1250) studied the mating patterns of rabbits and almost accidentally discovered the amazing ratio we now know as phi,” they narrate. The series, as you may know, has each number equal to the value of the sum of the preceding two numbers, as in: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 etc. “The sequence quickly settles down to the ratio scientists call phi, which is 1.618033989.” Phi is phenomenally important because it is the ratio associated with growth, explain the authors. “From flowers to human embryos and from seashells to galaxies – everything in the universe that grows expands outwards according to this fundamental rhythm.”

There is more to the world of Fibonacci than retracements, arcs, fans and timezones, says www.investopedia.com . “Every year new methods are developed for traders to take advantage of the uncanny tendencies of the market towards derivatives of the golden ratio.”

ARIMA (Auto-Regressive Integrated Moving Average), a forecasting model of Box and Jenkins, uses phi in its equation. Interestingly, www.hockey-fans.com has a page that discusses how the model can be used for forecasting ‘average goals per game in a season’.

Enthralling.

D. MURALI

http://BookPeek.blogspot.com