Why is mathematical constant pi so unique ?

• William Jones is the person, who introduced the symbol of Pi in the year 1706. But it was Leonhard Euler who popularized it in 1737.
• Pi has about 6.4 billion known digits which would take a person roughly 133 years to recite without stopping.
•  The world record holder for the most memorized digits of Pi took nine hours to recite over 44,000 digits of Pi.
• Some scientists use the fractions 22/7, 355/113  and 104348/33215 to approximate Pi. These fractions have an error of only 0.04025%, 0.00000849% and 0.00000001056% respectively. 
•  The Babylonians, who found the first known value of Pi, used the fraction 25/8. Although Pi can be approximated by a fraction, it cannot be expressed as a fraction because it is an irrational number. In other words, Pi’s digits go on randomly for infinite.
• It is impossible to 'square the circle'. In other words, you can't draw a square with the same area as a circle using standard straight-edge and compass construction in a finite number of steps. The Greeks were obsessed with trying to do this. A long time ago people thought there was an illness attached to trying to 'square a cirle' called Morbus Cyclometricus.
• If one were to find the circumference of a circle the size of the known universe, requiring that the circumference be accurate to within the radius of one proton, only 39 decimal places of Pi would be necessary.
• At position 763 there are six nines in a row. This is known as the Feynman Point.
• Pi day is celebrated on March 14 at the Exploratorium in San Francisco (March 14 is 3/14) at 1:59 PST which is 3.14159. Pi Approximation Day is on the 22/7 - that is, July 22. For the past few years, people at Chalmers University have celebrated it.
• There are people who believe that Pi contains the answer to the universe, or that information is held in the digits. It has even been suggested it contains the VOICE OF GOD. In Carl Sagan's book 'Contact' the places of Pi are found to contain a message from the beings that built the universe.
• With the help of Hitachi SR 8000, a powerful computer, a Japanese scientist found 1.24 trillion digits of Pi, breaking all the previous records.
• There are no zeros in the first 31 digits of Pi.
• First six digits of Pi appear in order at least six times among the first ten million decimals of Pi.