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The number π is a mathematical constant, the ratio of a circle's circumference to its diameter, commonly approximated as 3.14159.


Pi is easy to observe, but hard to compute accurately by hand.

You can measure Pi by constructing a physical wheel and rolling it out - but you won't get more than a digit or two of accuracy.

A chart of historical dates when the number of digits in Pi was discovered.

Year Digits Value
26th century BC - Ancient Egypt 3 22/7 = 3.14...
250 BC - Archimedes 3 3.1408
150 AD - Ptolemy 4 3.141666...
480 AD - Zu Chongzhi 6 3.1415926
1400 - Madhava of Sangamagrama 11
1424 Jamshid al-Kashi 16
1621 Ludolph van Ceulen + student 35
1699 71
1706 100
1794 137
1841 152
1844 200
1853 440
1874 - last before calculators 527

Why cell phones and modern communication wouldn't work without Pi.

We all take our cell phones and modern communication for granted nowadays.  Thanks to the discoveries and advancements in Pi over the centuries by men like ArchimedesIsaac Newton, and John von Neumann we were able to build on their work and develop modern technology and communications.

Cell phones use Pi based calculations to improve the speed and accuracy of voice-based communication.

A very important practical application is in the field of "signal processing”. A fundamental operation here is the “Fourier transform”, which converts a signal to a frequency spectrum. Your cell phone does a Fourier transform when it communicates with the local cell tower. Even your ear performs a Fourier transform (although not by digital computation) when it distinguishes sounds of different pitches, or when you recognize a friend’s voice. Mathematically speaking, the Fourier transform is the formula (don’t worry if you don’t understand how it works):

where e is Euler's Number, a famous mathematical constant equal to 2.71828..... Note that π once again appears prominently in this formula. This formula is evaluated digitally in your cell phone, by means of a certain clever algorithm, known as the “fast Fourier transform” or “FFT”, which was discovered by mathematicians in the 1950s (although Gauss may have inadvertently discovered it in the 19th century). It is quite likely that variations of the FFT algorithm are the most widely used numerical algorithm (i.e., computational scheme based on a mathematical formula) performed on computers worldwide. And yes, each of these involves π — in other words, your cell phone or smartphone has the numerical value of π somewhere buried in its computer logic, possibly in more than one place.

It has taken five centuries to effectively use Pi, we only need five minutes of your time to provide a great insurance quote.