2/18/2023 0 Comments Weird ways to calculate pi![]() ![]() Something is being illuminated, but it is far in the distance and instantly returns to darkness. It’s like standing in a desert at night and seeing flashes of lightning from a storm that lies over the horizon. I do not understand it, but while I am actively reading an explanation, I can glimpse how it might all make sense to someone who has achieved mathematical satori. It takes but a few paragraphs in the hands of someone who understands these abstractions to explain the basis for this profound identity. We then raise “e”, Euler’s number, which is also exotic and irresolvable, to the power of the product of i and pi. We take the exotic, irresolvable number pi and multiply it by the square root of the number (-1). “ i” is an “imaginary” number, the square root of (-1). Like pi, it can be calculated forever without resolving. Like pi, it is irrational and transcendental. It can be stated as the value of (1 + 1/n) n as n approaches infinity. “e” is “Euler’s number”, the “natural” logarithm. Most astounding to me is the number’s appearance in one of the most profound and beautiful statements of mathematics, one that combines seven basic symbols in the strangest way. The planets revolve around the sun along lines that can be calculated using pi. If you were to make a chart that showed the hours of daylight for each day over a year, the result would be a sine wave, a function dependent on pi. Yet this irrational, transcendental, incalculable number is present in nature in strange ways. It is also a transcendental number, meaning that there is no algebraic equation whose coefficients are rational numbers that will yield pi as the answer. It is an irrational number, meaning that it cannot be stated as the ratio of two whole numbers. Yet, the brothers or their descendants could continue to calculate for a century, or a millennium, or for as long as the earth lasts, and never fully state the number. They had found nothing at the time of writing.Īccording to the article, the brothers had calculated pi to such a level of precision that if you compared two circles, one a perfect circle with a circumference equal to that of the entire universe, the other a circle that you would get using their estimation of pi, the two circles spanning the universe would differ by the width of a molecule. They wanted to see if anywhere in this sequence of billions of digits there might be a pattern, some sequence that repeats. The sequence of digits never ends.Ī couple of years ago, I read an article about a pair of brothers whose life work was to calculate pi to the greatest precision possible. ![]() One of the oddities of the number is that you (or rather the nearest mathematician) can keep calculating to “Pi Millisecond” or “Pi Microsecond” or any level of precision you like. If you wait 26 ticks of the clock after you reach Pi Minute, you would be in “Pi Second” – 3.1415926. The approximation continues ……159, so 1:59 on March 14 would be “Pi Minute”. The approximation begins with 3.14, so today, March 14, is “Pi Day”. The number pi, or π, cannot be stated using conventional digits. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |