We now know 62.8 trillion decimal places of the number Pi



Defining the number Pi (π) is easy: it represents the ratio between the circumference of a circle and its diameter. Or, to put it another way, a circle of diameter 1 will have a circumference of length π. But how much is that, π? For school children, the answer is often 3.14. The most picky sometimes push up to 3.1416, a rounding far from the reality of this number, which until this week included 50,000 billion digits behind the comma. After 108 days of computing, a high-performance computer at the University of Applied Sciences in Graubünden, Switzerland, smashed this record by adding 12.8 trillion digits.

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By way of comparison, if we had to print the entire number π at this stage, that would represent some 62 million pounds, estimates Jean-Paul Delahaye, mathematician and computer scientist at the University of Lille (1). The national library of France has just under 16 million books and collections. ” Not only does no one ever print this number, but no one looks at it, continues the specialist. All these decimal places only exist for the computer that calculated them.

Unnecessary precision, but proof of computer advances

For enthusiasts, the last ten digits of π are now 7817924264. A great mathematical feat, but for what use? As summarized by Julia Collins, a mathematician at the Australian University Edith Cowan, in an article on The Conversation : “ Ten decimal places are enough to calculate the circumference of the Earth to within a millimeter. With 32 decimal places, we can calculate the circumference of the Milky Way with a precision of the order of the width of a hydrogen atom.. “

Knowing so many digits behind the comma therefore does not upset our daily life. It is just useful for mathematicians to know if π is a “normal” number, that is to say that each digit and series of digits return at a given frequency, according to given probabilities.

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In reality, as often in science, the result is less important than the means to achieve it. ” To break such records, it is necessary to develop algorithms capable of handling very long sequences of digits and technologies capable of calculating very quickly, without interruption and without error., explains Jean-Paul Delahaye. It is very useful in cryptography for example. »Computing, software and hardware power, which is also used in weather forecasts, biology or artificial intelligence.

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