How Did Pi Digits Come About? – Let’s Find Out

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History reveals existence of a fixed circumference to diameter ratio approximated at three; hence, pi digits. Further studies indicate that Archimedes used the initial theoretical pi digits test during his calculation.

Around 1761 Lambert ascertained that pi was indeed irrational; thus, should not be drawn as an integer number ratio. More so, in 1882, another revelation by Lindeman confirmed that pi was also transcendent. Hence, it cannot be used as an algebraic equation formula involving rational coefficients of any kind. This revelation ascertained that there is no way one can square a circle, an issue that affected most mathematicians during that time.

What is the actual number of pi digits? Does it have a limit?

The fact that pi is naturally irrational, it therefore implies that the numbers have no limit or can be repetitive in any way. However, pi digits’ computation tends to excite mathematicians across the globe. There those who spent the better part of their lives doing pi digits’ test.

Interestingly, before computers, they had managed to calculate. Until then, the number of calculated digits stood at below 1000.  A computer was able to calculate 2000 pi digits as of 1949, and more effort was being done to increase the number. As of 1999, the number of calculate pi digits has rose to millions (206,158,430,000), thanks to a supercomputer (University of Tokyo).

Pi Approximation

According to Archimedes, pi ranges between 3 1/7 and 3 10/71 (223/71<  < 22/7). To date, 22/7 remains a good calculation but 355/113 is considered a much better estimate.

Pi Related Websites

As it were, many people throughout the world constantly consider pi a great fascination. In case you wish to learn more about pi, you can visit check the various pi related web sites. There are those sites that provide pi digits ranging from thousands to billions. Others will offer you more info on people dealing with pi digit calculation, pi music, people with ability to memorize pi, pi clubs, pi demos and the like.

A Simple Pi Digits Test

While there are various ways one can use to understand more about pi, doing a pi digits test on your own is more fascinating. In this case, Buffon’s Needle is the most common one. This type of pi experiment allows you to drop a pointer on top of ruled paper sheet. If you monitor the number of times the pointer falls on a line, you will realize that it is directly linked to the pi value.

The Initial 100 Digits of Pi Test (Decimal Places)

If you are keen on working with pi, then here are the first 100 pi decimal places you should be able to work through:

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 …

These digits are endless, and go on forever!

Pi Formulas

Additional Complex Formulations and Derivations include:

Leibnitz’s Formula

PI/4 = 1/1 – 1/3 + 1/5 – 1/7 + …

Vieta’s Formula

2/PI = sqrt2/2 * sqrt( 2 + sqrt2 )/2 * sqrt(2 + ( sqrt( 2 + sqrt2) ) )/2 * …c

Lord Brouncker’s Formula

4/PI = 1 +        1


           2 +     32


               2 +   52


                  2 + 72

(PI2)/8 = 1/12 + 1/32 + 1/52 + …

(PI2)/24 = 1/22 + 1/42 + 1/62 + …

Wallis Product

PI/2 = 2/1 * 2/3 * 4/3 * 4/5 * 6/5 * 6/7 * …

2/PI = (1 – 1/22)(1 – 1/42)(1 – 1/62)…

Euler’s Formula

(PI2)/6 = SUM (n = 1..inf) 1/n2 = 1/12 + 1/22 + 1/32 + …

(or generally, more…)

SUM (n = 1..inf) 1/n(2k) = (-1)(k-1) PI(2k) 2(2k) B(2k) / ( 2(2k)!)

B(k) = the kth Bernoulli #. e.g. B0=1 B1=-1/2 B2=1/6 B4=-1/30 B6=1/42 B8=-1/30 B10=5/66. Additional Bernoulli numbers include (n 0)B0 + (n 1)B1 + (n 2)B2 + … + (n (n-1))B(N-1) = 0 supposing all odd Bernoulli numbers > 1 are = 0. (n k) = binomial coefficient = n!/(k!(n-k)!)

The Best Way to Remember the Pi 100 Digits

There are, of course, certain days of the year that you will find very exciting. For math lovers, the 14th of March is their most memoriable day. Maths enthusiasts across the globe celebrate Pi Day on this date.

During Pi Day celebration, there are so many things one can learn.  You have the opportunity to learn how to remember, go about a Pi 100 digits test, and more.  If you are lucky and a fast learner, it won’t take you long before you start singing the first pi 100 digits.

No matter your intentions – for personal challenge, epic contest, or in honour of the much-loved subject (maths) – you only need to find the right technique. Memorising a chain of digits is extremely tricky. It requires a high level of skill to accomplish the task.

As such, the Pi Mnemonic Major System (Phonetic Number System) plays a critical role in this respect. The classic method allows you to allocate to each number from 0 to 9 a dissimilar consonant sound. These relations of sound enables you to generate silly phrases and words that march directly to the sequense of digits you wish to memorize.

The most important thing to note here is the technique allows you to remember a pi digits string of your choice. If you are good at mastering things, then you will be  able to start remembering the numbers rightaway.

Bottom Line

While it may seem a tricky challenge, learning how to go about the pi 100 digits test is a big milestone. Note that life is mathematical, and there is no way we can ignore it. Thus, anything that falls into this exciting subject calls for our attention, and pi isnt an exception. Whichever way, remember that pi is critical for most mathematical formulations.  We must learn to live with it in all aspects, and memorizing the digits therein is essentially important.