listfoki.blogg.se - Who was the first to calculate pi

#Who was the first to calculate pi how to#
#Who was the first to calculate pi full#
#Who was the first to calculate pi Pc#
#Who was the first to calculate pi series#

Wow! I must have really annoyed you by what I wrote. Re: Enough with the term "million million"! This is what lack of funding does to american education (now a contradiction in terms). To salvage any intelligence, at least describe it to the tenth power, instead of thinking that saying the same word twice somehow multiplies it's meaning.

#Who was the first to calculate pi how to#

Those who even speak "million million" are simply retarded and do not know how to quantify numbers higher than a million.The same applies for those who say "billion billion", who cannot quantify a quintillion. The term "a million million" is easily quantified by a 2nd-grader as a "trillion".For christ's sake, we don't say, "a thousand thousand" to describe "a million", unless I am 14 centuries ahead of my time and I didn't know it.

Lim Bio Liong for his excellent program that allowed me to capture the window snapshot above.

Getting a computer to calculate lots of digits of pi does have its uses, it can be used to show that the computer, or at least its ALU, is working properly. I know it's pretty straightforward but I thought people might be interested in seeing it. By changing to #define NDecimalPlaces (1000), you can now achieve in a fraction of a second more than William Shanks failed to achieve in 15 years. In 1944 it was found that he had made a mistake in the 528 th place, and all the following digits were wrong.

The 19 th century English mathematician William Shanks spent over 15 years calculating the first 707 places of pi using Machin's formula.

The first 1,000,000 decimal places of pi were first calculated in 1973.

Comparison with this shows that the last three decimal places are wrong, so we have actually got pi correct to 1,000,101 decimal places.

#Who was the first to calculate pi series#

This actually gives us 1,000,104 decimal places, but the last few might be incorrect because of the infinite number of terms of the Maclaurin series that we have to throw away. To get 1,000,000 decimal places, each multi-length number is implemented as an array of 166685 integers, using a base of 1,000,000 so that each integer gives us 6 significant digits.That works out at about 380 million million instructions in total.

#Who was the first to calculate pi Pc#

My 7,000 MIPs PC took about 15 hours to calculate the first 1,000,000 decimal places of pi. So 10 times as many decimal places will take about 100 times as long.

The algorithm described above has an O(n 2) duration.The answer is written to a file called result NDecimalPlaces.txt. You can adjust how many decimal places it calculates by changing #define NDecimalPlaces (1000100) to some other number. The attached program is a straightforward Win32 Console Application (it started out as the standard "Hello, World!" application with MFC support). Looks like it's just dividing term5m by a number, but it's actually calling CRHMultiLengthInteger::operator /=().

#Who was the first to calculate pi full#

I've made full use of the operator notation in C++ to make the code look like we're just working with ordinary numbers. The multi-length numbers are wrapped up inside the class CRHMultiLengthInteger. To get one million decimal places, I've done a simple implementation of the multi-length arithmetic operations that I need, using a big array of ints. Multi-length arithmeticĪ 32-bit integer only gives us about 9 significant digits. To get 1,000,000 decimal places accuracy for pi, we need about 715,000 terms of the tan -1(1/5) series and about 210,000 terms of the tan -1(1/239) series, but this doesn't have to be worked out in advance, the attached program stops automatically when it determines that the required accuracy has been reached. īy including sufficiently many terms of this series, we can achieve any desired accuracy. Tan -1() is the Inverse Tangent function, and I use the Maclaurin series to calculate it: I've chosen a method that is fairly simple and converges reasonably fast. Some are simple to implement but converge very slowly. Some methods converge rapidly but are complicated to implement.

I'm not going to try to write pi as the Greek letter in this article, because some browsers might show it incorrectly. It is an infinitely long non-recurring decimal number. It is defined as the ratio of a circle's circumference to its diameter, but it crops up in all sorts of places in mathematics. Pi is one of the most important numbers in mathematics.