Of Pi and Phi...

One would think that there are enough number (or infinite!) of things to marvel at in this world. Sure but leading them is the confounding - yup, highly perplexing - is the order in chaos:  Like the atoms and the smallest matter ever - quarks - and how everything is made up of the same stuff with the small (vast) difference being in their electron numbers. But that's a piece for another day!

Today one would like to talk about Pi and Phi. The Pi or pi is also known as 'Archimedes Constant. Go figure! 

The Pi which is a Greek letter was used by Euler in early 1700. But it was discovered by the Babylonians in 200 - 4000 BCE. The Chinese and Indians too claim discovery and the jury is still out on this but it is a a certainty that Pi is true and it is true by 3.17..... with the decimals leading to infinity!

 π

“Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number pi”  ~William L. Schaaf, Nature and History of Pi

What is Pi?  The number π is defined as the ratio of a circle's circumference to its diameter, and it also has various equivalent definitions. It is approximately equal to 3.14159. Pi has now been calculated to 31 trillion digits.  The first 39 decimals are needed to be able to perform all calculations with virtually no error.  

 

No matter how big or small a circle - Pi is constant. Makes you think...

There is a day to celebrate the unique number and it is called Pi Day. (Not Pie Day!) It falls on March 14 and can ( as I like to put it!) also be written as Ides of March Minus one day.

The other number or sequence is similar but different  and another example of how the world is organized. It is also called the golden ratio! And Beauty is the result. ( yes, you can judge a person's beauty using the golden ratio!). Some artists swear the Golden Ratio makes the most pleasing shape.

It has the 2!st Greek letter to signify it. It is called Phi or φ

It is also widely known (or close to) as the Fibonacci Sequence!

While Pi is pronounced with a P, Phi is done so with a F. Simple? 

What is Phi?

Phi is to a straight line what Pi is to a circle. Phi is 1.618.... is the ratio of the line segments that result when a line is divided in one very special and unique way. The Fibonacci sequence appears all over nature but some are still cynical.

It is also easily denoted by (close!) - 

There is a special relationship between the Golden Ratio and the Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... when we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio. In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation.  That is the reason I think they can be linked together.

The Golden Ratio is the most irrational number. And Pi is pretty close.

The Golden Ratio is also sometimes called the golden section, golden mean, golden number, divine proportion, divine section and golden proportion.