September 10

Pi To 62.8 Trillion Digits Useless And Fascinating

Pi To 62.8 Trillion Digits Useless And Fascinating

This week, University of Applied Sciences Graubunden in Switzerland set a new world record by calculating the number of digits of Pi. It was 62.8 trillion numbers. My estimate is that these numbers would have filled every book in the British Library ten-fold if printed. This feat of arithmetic by the researchers took 108 days, 9 hours, and is far more impressive than the January 2020 record of 50 trillion numbers

Why Do We Care Pi?

Pi (the mathematical constant) is the ratio between a circle’s diameter and its circumference. It is about 3.1415926536. These ten decimal places all that is need to calculate Earth’s circumference with a precision of less then a millimetre. We could calculate the circumference our Milky Way galaxy with 32 decimal places to the same precision as the width of a hydrogen Atom. With only 65 decimal points, we could calculate the size of the universe to within a Planck length. This is the shortest distance that can be measure.

The remaining 62.79 trillion numbers are of no use. The short answer is they aren’t scientifically useful. However, computer scientists and mathematicians will eagerly await the details of this massive computation for many reasons.

Why Is Pi So Intriguing?

Although the concept of pi is easy enough to understand for primary school students, its numbers are notoriously difficult to compute. One number such as 1/7 requires infinitely many decimals to write down, 0.1428571428571… but the numbers repeat themselves every six positions, making it simple to understand. Pi is an example of an irrational numerical number that has no repeating patterns. Pi is not only irrational but transcendental. This means that it cannot be define by any equation containing whole numbers.

Since ancient times, mathematicians have been computing pi worldwide. However, techniques for doing so changed drastically after the 17th-century with the introduction of calculus and the infinite series technique. Madhava series, named after Madhava of Sangamagrama, an Indian-Hindu mathematician, is one example.

p = 4 (1 – 1/3 + 1/5- 1/7 + 1/11 +)

Adding More Terms

This computation is closer to pi’s true value by adding more terms. It takes a while after 500,000 terms it only produces five correct decimal places for pi!

New formulae for pi are a way to improve our mathematical knowledge and allow mathematicians to compete for bragging rights. In 1988, the infinite sum was discover and can calculate 14 new pi digits for every term that is added.

Breaking the record is a motivator for new digits, but there are other important benefits.

The first is the testing and development of supercomputers as well as new high-precision multiplication algorithms. The optimization of the computation of pi results in computer hardware and software that can benefit many other areas, such as accurate weather forecasting, DNA sequencing, and COVID modeling.

The most recent calculation of pi was 3.5x faster than the previous attempt, despite 12 trillion more decimal places. This is an amazing increase in supercomputing performance within just 18 months.

Involves The Investigation

The second involves the investigation of the nature of pi. There are fundamental questions that remain despite centuries of research into the nature of pi’s digits. Pi is consider a normal number. This means that all possible sequences should be equally common.

We expect that the digit 3 will appear as frequently as the number 8, and the string of digits 12345 to occur as often or more often than 99999. We don’t know if every decimal digit in pi appears infinitely frequently, or if there are more complicated patterns.

Researchers are still waiting confirmation from Guinness Book of Records. We hope that there will be many mathematically fascinating treasures in the numbers.

The digits pi will not be finished there will always more data to discover and new records to break. If you don’t have a supercomputer but are interested in computing decimal numbers (and a PhD), you might consider other interesting irrational number like 3, which is only known to be 10 billion digits, the tribonacci constant (20,000) or the Twin Prime Constant (1.001 digits). Although you may not be featured in the morning news, it is a way to get your name into the record books.

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Posted September 10, 2021 by lile in category "Uncategorized