What is pai in math

The number Pi - fascination in numbers

π - a never-ending story - irrational, transcendent and fantastic

The first 500 digits / decimal places of the circle number pi:
1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 …

Memorizing the first 100 digits of pi is sufficient for admission to the Club of Friends of the Number Pi. If you are looking for even more Pi digits, there are 1000 digits after the decimal point up to a million digits, everything a number lover's heart desires.

The Circle number pi - the most famous number in the history of mathematics

pi (π) describes the ratio of the circumference to the diameter of a circle

There are many formulas in which π plays the leading role. Be it when calculating the circumference of a circle (U = π d = 2 π r), or the area of ​​a circle (F = π r2), Volume (V = 4/3 π r3) or the surface of spheres, cylinders, cones, etc. And so it is clear that if there is any number that is really round, then it is the magic circle number π.

First simple formulas for calculating pi

The story of pi begins with the ancient Egyptians. The Greek Archimedes succeeded approx. 250 BC. The first geometrical derivation of Pi on the basis of n-vertices. But it was not until the end of the Middle Ages that the first formulas for more precise calculation of the circle number appeared. In honor of Ludolph van Ceulen, who calculated π to 35 decimal places in 1596, π is now also known as Ludolph's number. There are infinitely many formulas for calculating pi. Perhaps the simplest and most amazing and oldest Formula for π likely the so-called Leibniz series be:

The series is a special case of the arctangent series (π / 4 = arctan 1) and was (re) discovered by Gottfried Wilhelm Leibniz in 1682. Unfortunately, this series converges very poorly, which is why it is not suitable for calculating the sequence of digits of the circle number in practice.

About 25 years later (1706) John Machin succeeded in deriving a much faster converging sequence from the arctangent series with the aid of the addition theorem.

On the basis of this formula, he calculated pi to 100 digits in 1707. This record lasted for 12 years.

It went on in small steps. It was not until 1949 that the 1000 digit limit was exceeded. G. W. Reitwieser from the USA managed this feat on an ENIAC machine. Then it happened in quick succession, thanks to ever faster computers and formulas. In 1972 it was possible to calculate pi up to 1,000,000 decimal places, in 1989 the billion mark fell and currently the pi calculation world record already stands at an unbelievable 50 trillion decimal places and is held by the American IT specialist Timothy Mullican. I try to follow the further development of the Pi Records here in the blog. And since the number pi is infinitely long, this record hunt will never come to an end 😉

Approximate values ​​for pi

Pi is infinitely long, Pi's digits do not repeat and do not follow any pattern. In this respect, a person will never be able to write out all the digits of Pi. Of course, mathematicians and number freaks were always looking for good approximate solutions for the value of pi. The simplest and easy to remember approximation formula should be the fraction 22/7 = 3.1428…. This value is accurate to 2 decimal places. The fraction 355/113 = 3.1415929 ... with a remarkable 6 correct decimal places is also still quite compact. For 9 correct digits, we end up with 103993/33102 = 3.14159265301… with a practical, but no longer quite so noticeable approximation.

Pitoresque memory acrobats

There are currently two Indians who can freely recite 70,000 digits of Pi from memory. Suresh Kumar Sharma holds the current world record with 70,030 digits. Incidentally, reciting the digits took over 17 hours.

The Digits of π - Pi Edition - Chaos written in numbers

Pi is even available in printed form. As a pi book, so to speak. Hundreds of pages filled with the digits of pi. The chaos in numbers poured onto paper 😉

-> Pictures from the PI edition

Approx. 2.5 million digits of the number Pi in black letters. The ideal gift for the inclined mathematician and pi fan.


My Pi Edition - 3.14159265358979323846264338327950

I have been the proud owner and author of my own PI book since February 2015. There is a lot to Knoff-Hoff in this book, so I think I can call it the best PI book on the market. It is exactly the book that I would have liked to have given myself. Which I did in the end 😉

A reason to celebrate - the Pi holiday

To celebrate PI Day (date in American notation: 3/14), Americans like to serve their pi friends a pie. Both pi and pie are pronounced like pai (or pei) in English. By the way, in 2015 we celebrated 3/14/15, a combination that only occurs every hundred years 🙂

While Pi is probably the most famous number in the history of mathematics, the Pythagorean theorem (a² + b² = c²) is probably the best-known theorem of mathematics. And the two celebrities get along well, Pythagoras his right-angled triangles can be conveniently placed in a circle and even used for approximate calculations of pi.

Danger. The number Phi Φ is often confused with the number Pi, which can be easily read in analyzes of Google search queries. Phi, however, refers to the golden ratio and not to the circle.

e ^ (i * π) + 1 = 0

Note on image rights:
Animated rolling of the circumference, which illustrates the number π - @John Reid - Wikipedia (the GNU Free Documentation License)
PI number written in red - 3D - @ pixelfabrik - Canstockphoto
Pi Pie (a π-cake with 27 decimal places), made at the Technical University of Delft (public domain)

© 2019 Gerald Steffens