PI number – a real non-quantifiable constant All over the world, it is one of the ways of spending the PI Day celebrations, which also include competitions, games, and lectures on issues and secrets of mathematics, physics and other technical sciences where we can see the presence of the number PI. Why pies actually? Because of an innocent play on words – the number PI is pronounced the same as pie. On he celebrated this holiday with his co-workers by walking with them in a circle-like procession, and at 13:59 GMT-8, according to the record 1:59 PM he proceeded to consume fruit pies in the shape of a circle. The initiator of the PI celebration was an American physicist named Lawrence N. The event received overwhelming support from the US House of Representatives. How can we celebrate the PI Day?Īlthough the number PI has been known to mankind since Ancient Greece, the initiative to celebrate the number PI first saw the light of day in 1988 at the Exploratorium science museum in San Francisco, USA. Interestingly, this day has another symbolic meaning – the 14th of March is also the birthday of Albert Einstein – the famous scientist who was an eminent specialist in theoretical physics, with a particular emphasis on quantum mechanics and field theory. “3,14” – the digit “3” because March is the third month in order according to the Gregorian calendar scheme, in which a year has 12 months formed by 365 days (366 days every four years in a leap year – the nearest leap year will be 2022), and after the comma “14” – because the PI number holiday is celebrated on the 14th of the month.
The choice of this date is not accidental and it refers to the first three digits of the number PI, i.e. The PI holiday is celebrated on the same date every year, which is the 14th day of March. It is a value without which mathematics, physics and other sciences and technology based on them could not do without. The number PI is probably the most popular mathematical constant – so much so, that the calendar has a holiday devoted to it – PI Day.
However, the Adamchik-Wagon reference shows how similar relations can be discovered in a way that the proof accompanies the discovery, and gives a 3-term formula for a base 4 analogue of the BBP result. The BBP formula was discovered using the PSLQ Integer Relation Algorithm. More details can be found in the Bailey-Borwein-Plouffe reference. This yields the hexadecimal expansion of Pi starting at the (N+1)-th digit. The other sums in the BBP formula are handled similarly. Not many more than N terms of this sum need be evaluated, since the numerator decreases very quickly as k gets large so that terms become negligible. Division by (8k+1) is straightforward via floating point arithmetic.
#Who was the first to calculate pi mod#
The numerator of a given term in this sum is 16 N-k, and it can be evaluated very easily mod (8k+1) using a binary algorithm for exponentiation. We are interested in the fractional part of this expression. For simplicity, consider just the first of the sums in the expression, and multiply this by 16 N. Here’s a sketch of how the BBP formula can be used to find the N-th hexadecimal digit of Pi. You might start off by asking students how they might calculate the 100-th digit of pi using one of the other pi formulas they have learned. This is far better than previous algorithms for finding the N-th digit of Pi, which required keeping track of all the previous digits! Moreover, one can even do the calculation in a time that is essentially linear in N, with memory requirements only logarithmic in N. The reason this pi formula is so interesting is because it can be used to calculate the N-th digit of Pi (in base 16) without having to calculate all of the previous digits! Here is a very interesting formula for pi, discovered by David Bailey, Peter Borwein, and Simon Plouffe in 1995:
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