Billion Digit Pi

Greek letter Pi

Pi is probably the best known number in mathematics and is equal to the number of times a circle's diameter will fit around its circumference. This page by G F Cornwell offers the first billion digits of Pi and finds calendar dates within Pi.

Here is the value of Pi accurate to 30 decimal places.

3. 1415926535 8979323846 2643383279

  Birthdays in Pi

Pi has an infinite numer of decimal places so if you search far enough you can expect to find any sequence of digits.

For example, if your birthday is 25 Dec 1991 then you may be interested in finding the digits 25 12 1991.

Use the form below to find the location of your birthday.

Birthday Cake

Birthday Statistics

The graphic shows the distribution of birthday ages submitted to this page over a 3 month period.

Age Distribution

  Pi = 22/7 ?

Pi can never be exactly equal to the value of a simple fraction. However, you can find fractional values that are increasingly close to Pi as the two numbers of the fraction are increased in value.

The fractions below are good approximations to Pi. The bold digits in the decimal values are the same as those in Pi.

22 / 7 3.142857142857
355 / 113 3.1415929203539823
312689 / 99532 3.1415926536189366233
21053343141 / 6701487259 3.1415926535897932384623817427748

Notice that the six digit sequence 142857 in the value of 22/7 repeats. In fact this sequence recurs, or repeats indefinitely. If you expand the value for 355/113 you will find this also recurs, this time after 112 decimal places. This is a property of all fractions, but an irrational number like Pi will never recur.

  An Elegant Equation

(from) Euler's Equation

This small equation brings together 3 important numbers from disparate fields of pure mathematics. Pi from geometry, e from calculus (the base of natural logarithms) and i , the basis of complex number theory.

The equation was discovered by the mathematician Leonhard Euler in the eighteenth century.

  How is Pi Calculated?

Pi is calculated by adding the terms of an infinite series like the one below.

Pi = 4 - 4/3 + 4/5 - 4/7 + 4/9 .......

This series was found by the German mathematician Leibnitz in the 17th century. It is not a good choice for calculating Pi because a large number of terms is needed to get an accurate answer. Better series, for example those discovered by the Indian mathematician Ramanujan, converge quickly to an accurate value because each term is very much smaller than the previous one.

By 1700 the first 100 digits of Pi had been calculated manually. Then in 1949 an early computer ENIAC was used to calculate Pi to 2037 decimal places in 70 hours. A modern (2005) personal computer with a 2GHz processor can calculate a million decimal places in less than a minute.

  Useful accuracy?

The calculation of Pi has long interested mathematicians. Even the great scientist Isaac Newton admitted to spending a large amount of time calculating Pi, by hand, to 15 decimal places. By 2005 more than one trillion (1,000,000,000,000) digits of Pi had been calculated, but is this of any real use?

For practical calculations, for example to estimate the weight of an iron sphere of known diameter, only the first 20 digits of Pi are ever likely to be needed. This is because we are unable to measure anything to this accuracy. For example, the density of iron is not known precisely, nor could the diameter of a sphere be measured with this precision. Fundamental constants like the speed of light can only be measured to about 12 digit accuracy and the gravitational constant that allows the calculation of the force between two iron spheres is still only known to 5 digit accuracy.

  One million digits

Show me in a new window:
The first 10000 digits of Pi

The first 100000 digits of Pi
The second 100000 digits of Pi
The third 100000 digits of Pi
The fourth 100000 digits of Pi
The fifth 100000 digits of Pi
The sixth 100000 digits of Pi
The seventh 100000 digits of Pi
The eighth 100000 digits of Pi
The ninth 100000 digits of Pi
The tenth 100000 digits of Pi

  One billion digits


Comments Geoff Cornwell  
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