Mysterious Number: π
By Dr. Muhtar Ahat

Throughout the history of five thousand years of civilizations, most fascinating, mysterious, and important number is π=3.141592653…… The question arises from such a simple problem: Draw a square that exactly covers the same area as a circle, using a straight rule and a compass. Human have been struggling to find a mathematical, geometrical relationship between the circle and the square for centuries. But, they failed.

Pi by definition is the ratio of circumference to the diameter of a circle. The earliest-known record of this ratio was written by an Egyptian named Ahmes around 2000 BC. He tried to construct a square that has the same area as the circle. He gave the ratio of circumference to diameter as 256/81 or 3.16049. It was off less than 1% from the value of what we using now: 3.141592…… The great Pyramid at Giza also has a fascinating relationship inherent in its structure. The ratio of the length of one side to the height is approximately π/2.

The π is a most interesting number in the mathematics. Just as Len Berggren et al. said at their book <<Pi: A Source Book>>:” The computation of π is virtually the only topic from the most ancient stratum of mathematics that is still serious interest to modern mathematical research.” Many mathematicians have dedicated years of the lives (some of them spent their whole life) to churning out as many digits as possible. The current record is 51 billion digits. It is achieved by the incredible power of both brain and computer.

Pi teaches us about the limits of our own comprehension. It marks the boundary between the finite and infinite. It appears throughout math, physics, statistics, engineering, architecture, biology, astronomy, arts and even our daily life. There is no doubt about that if we understand this number better, we’d have a deeper understanding of math and physics of our universe.

You may find ease way to calculate Pi by yourself up to 6 or 7th places. One simple way: make a polygon inside of a circle and calculate the perimeter of polygon. Then compare to the circumference of circle. You will find real good approximations with the helping of a good calculator. For instance, hexagon gives π ≈ 3; 12-side polygon gives; 24-side polygon yields ; 48-side polygon gives ; 96-side polygon gives ; ……

Here, we listed a simplified chronology of π for reference. If anyone interests on more information, go to the www.joyofpi.com.

 

A Pi chronology

 Year                              Name

2000 B. C. E                  Egyptians use π=256/81=3.1605

1100 B. C. E                  Chinese use π=3

550   B. C. E                  Old Testament implies π=3

3rd centuries B. C. E       Archimedes uses a 96-sided polygon to establish
                                                  

 

  450                               Tsu Chung-chih establishes 355/113

1593                               Francois Viete finds first infinite product to describe Pi; Adriaen Romanus finds to 15 decimal places

1748                               Euler’s theorem and many series for π

1794                               Georg Vega calculates π to 140 decimal places

1949                               ENIAC computers 2037 decimals in 70 hours

1961                                                              Daniel and John compute to 100,200 decimals in 8 hours

1989                                                              Chudnovskys calculate 1 billion digits

1997                               Kanada calculates 51 billion digits