Phi: The Golden Number

Phi (Φ), the term was first used by an American mathematician Mark Barr for denoting the golden ratio. Though the term was coined in the 1990s but the existence of this ratio could be traced back to 500 BC, and may be before. The ratio has always exited in mathematics and design. The Greeks and Egyptians used the ratio in architecture, in fact Leonardo Da Vinci used the ratio in his art work (visible in the “Last Supper” and many more) . Enough with the history!!

The ratio can be simply defined as: 

The ratio of the length of a line segment AB to it’s section AC, if the ratio AB/AC is equal to AC/BC i.e.

AB/AC = AC/BC

The ratio can also be defined using the golden rectangle (1 x Φ), where if we cut a square of unit length, the remaining rectangle will be similar to original rectangle i.e.

1/Φ = (Φ-1)/1 

Rearranging the above two, we get a quadratic equation, the positive root of which is Φ.

In this blog, we will try to explore the different occurrence of Phi(Φ) in mathematics with a hope of discovering something new.