Bored mathematicians just calculated pi to 62.8 trillion digits
Swiss scientists just broke the record for counting pi
What makes pi so fascinating?
The concept of pi is simple enough for a primary school student to grasp, yet its digits are notoriously difficult to calculate. A number like 1/7 needs infinitely many decimals to write down – 0.1428571428571… – but the numbers repeat themselves every six places, making it easy to understand. Pi, on the other hand, is an example of an irrational number, in which there are no repeating patterns. Not only is pi irrational, but it is also transcendental, meaning it cannot be defined through any simple equation featuring whole numbers.
Mathematicians around the world have been computing pi since ancient times, but techniques to do so changed dramatically after the 17th century, with the development of calculus and the techniques of infinite series. For example, the Madhava series (named after the Indian-Hindu mathematicianMadhava of Sangamagrama), says:
By adding more and more terms, this computation gets closer and closer to the true value of pi. But it takes a long time — after 500,000 terms, it produces only five correct decimal places of pi!
The search for new formulae for pi adds to our mathematical understanding of the number, while also letting mathematicians vie for bragging rights in the quest for more digits. Theinfinite sum used in the 2020 recordbreaking effortwas discovered in 1988 and can calculate 14 new digits of pi for each new term that is added to the sum.
While breaking the record may be one of the key motivators for finding new digits of pi, there are two other important benefits.
The first is the development and testing of supercomputers and new high-precision multiplication algorithms. Optimizing the computation of pi leads to computer hardware and software that benefit many other areas of our lives, from accurate weather forecasting to DNA sequencing and even COVID modeling.
The latest computation of pi was 3.5 times as fast as the previous effort, despite the extra 12 trillion decimal places – an impressive increase in supercomputing performance in just 18 months.
The second is the exploration of the very nature of pi. Despite centuries of research, there are still fundamental unanswered questions about the way its digits behave. It is conjectured that pi is a “normal” number, meaning all possible sequences of digits should appear equally often.
For example, we expect the digit 3 to appear as often as the digit 8, and the digit string “12345” to appear as often as “99999”. But we don’t even know if each decimal digit appears infinitely often in pi, let alone whether there are more complex patterns waiting to be discovered.
The data for the new pi computation has not yet been released, as the researchers are awaiting confirmation from the Guinness Book of Records. But we hope there will be many mathematically interesting treasures within the numbers.
We will never “finish” computing the digits of pi – there will always be more to find and new records to break. If you don’t happen to own a supercomputer, but you have a thirst for computing decimal digits (and a PhD in mathematics), why not try other interesting irrational numbers like√3(only known to 10 billion digits), thetribonacci constant(20,000 digits), or theTwin Prime Constant(1,001 digits). You may not make the morning news, but it’s arguably an easier way to write yourself into the record books.
This article byJulia Collins, Lecturer of Mathematics,Edith Cowan University,is republished fromThe Conversationunder a Creative Commons license. Read theoriginal article.
Story byThe Conversation
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