What is a Nilakantha series?
Nilakantha attributes the series to an earlier Indian mathematician, Madhava of Sangamagrama, who lived c. 1350 – c. 1425. Several infinite series are described, including series for sine, tangent, and cosine, which are now referred to as the Madhava series or Gregory–Leibniz series.
What is the infinite series for pi?
A stunning solution of the mystery was discovered by Indian mathematicians about 1500 ce: π can be represented by the infinite, but amazingly simple, series π4 = 1 − 13 + 15 − 17 +⋯. They discovered this as a special case of the series for the inverse tangent function: tan−1 (x) = x − x33 + x55 − x77 +⋯.
What is an estimate of π?
Practical approximations Depending on the purpose of a calculation, π can be approximated by using fractions for ease of calculation. The most notable such approximations are 22⁄7 (relative error of about 4·10−4) and 355⁄113 (relative error of about 8·10−8).
How do you find pi with n digits?
Pi = SUMk=0 to infinity 16-k [ 4/(8k+1) – 2/(8k+4) – 1/(8k+5) – 1/(8k+6) ]. 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!
How do you find pi in python?
Approach:
- Initialize k=1 // this variable will be used as the denominator of leibniz’s formula, it will be incremented by 2.
- Initialize sum=0 // sum will add all the elements of the series.
- Run a for loop from 0 to 1000000 //at this value, we get the most accurate value of Pi.
How do I calculate pi on my computer?
With better computers and more efficient (but more complicated) infinite series formulas, pi has been calculated to over 13.3 trillion digits!…Using Your Computer to Calculate Pi.
| 01 | # Pi Calculator |
|---|---|
| 33 | # find pi using Machin’s Formula pi = 4 * (4 * arccot(5) – arccot(239)) |
| 34 | # and the power formula for arccot (see arccot function above) |
Is pi crypto infinite?
Value of Pi can never reach to Bitcoin. The main reason is that total Bitcoin supply is 21 million. On the other hand Supply of Pi Coins is in Billions.
Who is Nilakantha and what did he do?
Nilakantha was a mathematician and astronomer from South India who wrote texts on both astronomy and infinite series. Nilakantha was born into a Namputiri Brahmin family which came from South Malabar in Kerala.
Which is the infinite series of arctan x?
Thus, arctan x has an infinite series representation for Ix I < 1: 3 X5 arctan x = x- – + – – . (2) The series for -r/4 is obtained by setting x = 1 in (2).
Which is the main caste of Nilakantha Somayaji?
Nilakantha was born into a Namputiri Brahmin family which came from South Malabar in Kerala. The Nambudiri is the main caste of Kerala. It is an orthodox caste whose members consider themselves descendants of the ancient Vedic religion.