Phi Day: Discovering the Golden Ratio

Phi is arguably one of the most important mathematical constants. Phi is approximately 1.61803 and often referred to as the ‘golden ratio’. It has been studied since at least 300 BCE, when it was defined by Greek mathematician Euclid. It is found all over in nature, from snail shells and flower seed heads to many plant patterns such as those in pineapples, ferns and pinecones.


And, it plays a key role into aesthetics and architecture. From the great pyramids to the Parthenon, this number appears in the shapes and scales of many engineering designs and architectural feats. In art, this constant is used to quantify aesthetic beauty, such as in da Vinci's Mona Lisa, or even the face of a beautiful person.


Recently, lower secondary students have been discovering the mathematical constant phi, the golden ratio, through hands-on activities. They measured dimensions of "natural objects"—a star, a nautilus shell and human hand bones—and calculate ratios of the measured values, which are close to phi.


Then students learned a basic definition of a mathematical sequence, specifically the Fibonacci sequence. By taking ratios of successive terms of the sequence, they found numbers close to phi. They then solved a squares puzzle that creates an approximate Fibonacci spiral.

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