In 2021, Bert de Groot, Professor of Governance and Strategic Investment Policy at Erasmus School of Economics, published a paper in “Technological Forecasting and Social Change” titled “Disentangling the enigma of multi-structured economic cycles - A new appearance of the golden ratio.” In his paper, De Groot examines the economic cycles of GDP growth in over two dozen … [Read more...]

Using the Golden Ratio to win at football. The golden ratio is found in many places, but here's one you might not have expected: It can be found in football gaming strategy when making the "point after touchdown" decision as to whether to kick for 1 extra point or go for a 2 point conversion. This applies to the situation when a team is trailing by 14 points late in a … [Read more...]

Human expectations occur in a ratio that approaches Phi. Changes in stock prices largely reflect human opinions, valuations and expectations. A study by mathematical psychologist Vladimir Lefebvre demonstrated that humans exhibit positive and negative evaluations of the opinions they hold in a ratio that approaches phi, with 61.8% positive and 38.2% negative. Phi and … [Read more...]

Phi relationships appear in foreign currency price movements. It has long been known that phi and Fibonacci relationships appear in the stock markets.  The foreign exchange market, or Forex, is the largest market in the world.  The simplest definition of foreign exchange is the changing of one currency to another.  Since there are no touchable commodities affected, this is the … [Read more...]