2/21/2023 0 Comments Who was the first to calculate pi![]() “This is a benchmarking exercise for computational hardware and software,” he says. “World records: they’re not useful by themselves, but they set a benchmark and they teach us about what we can achieve and they motivate others. Given that even calculating pi to 1,000 digits is practical overkill, why bother going to 62.8tn decimal places?ĭe Gier compares the feat to the athletes at the Olympic Games. 62.8tn digit accuracy – what’s the point? Mathematicians have estimated that an approximation of pi to 39 digits is sufficient for most cosmological calculations – accurate enough to calculate the circumference of the observable universe to within the diameter of a single hydrogen atom. “I can’t imagine any real-life physical application where you would need any more than 15 decimal places,” he says. “When you’re playing an MP3 file or watching Blu-ray media, it’s using Fourier transforms all the time to compress the data.”įourier analysis is also used in medical imaging technology, and to break down the components of sunlight into spectral lines, de Gier says.īut, says Harvey, there’s a big difference between calculating pi to 10 decimal places and approximating it to 62.8tn digits. Pi is also crucial to something in mathematics called Fourier transforms, says Harvey. The constant appears in Euler’s identity, e iπ + 1 = 0, which has been described as “ the single most beautiful equation in history” (and has also featured in a Simpsons episode). ![]() “You can’t escape it,” says David Harvey, an associate professor at the University of New South Wales.įor example, the solution to the Basel problem – the sum of the reciprocals of square numbers (1/1 2 + 1/2 2 + 1/3 2 and so on) – is π 2/6. “Knowing pi to some approximation is incredibly important because it appears everywhere, from the general relativity of Einstein to corrections in your GPS to all sorts of engineering problems involving electronics,” de Gier says. Jan de Gier, a professor of mathematics and statistics at the University of Melbourne, says being able to approximate pi with some precision is important because the mathematical constant has many different practical applications. What is it good for? Absolutely everything The bill, whose purpose claimed to be a method to square a circle – a mathematical impossibility – almost enshrined in law that π = 3.2. In 1897, the Indiana Pi Bill in the US almost did away with fussy strings of decimals altogether. The amateur mathematician William Shanks, for example, calculated pi by hand to 707 figures in 1873 and died believing so, but decades later it was discovered he’d made a mistake at the 528th decimal place. He once jokingly claimed that if he had to recite pi digits he would name them up to this point and then say “ and so on”.It is a transcendental, irrational number: one with an infinite number of decimal places, and one that can’t be expressed as a fraction of two whole numbers.įrom ancient Babylonian times, humans have been trying to approximate the constant that begins 3.14159, with varying degrees of success. This block of nines is famously called the “Feynman Point” after the Nobel Prize-winner Richard Feynman. The chance of this happening if pi is normal and every sequence of n digits is equally likely to occur, is 0.08%. For example, at position 768 in the pi digits there are six 9s in succession. We need to remember the surprising fact that if pi was normal then any finite sequence of digits you could name could be found in it. His results imply that these digits seem to be fairly evenly distributed, but it is not enough to prove that all of pi would be normal. From the tests performed so far, it is still an open question whether pi is normal or not.įor example in 2003, Yasumasa Kanada published the distribution of the number of times different digits appear in the first trillion digits of pi: Digit Occurrences By looking at the digits of pi and applying statistical tests you can try to determine if it is normal. ![]() It isn’t randomly positioned.īut we can ask the related question: “ Is pi a normal number?” A decimal number is said to be normal when every sequence of possible digits is equally likely to appear in it, making the numbers look random even if they technically aren’t. So you can’t ask what the probability would be of a different number taking this position. For example, the second decimal place in pi is always 4. The reason we can’t call pi random is because the digits it comprises are precisely determined and fixed. ![]()
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