I would like to print e.g. 1000 or 2000 or 15000 decimals of pi value using R?
Now I get only six
> pi
[1] 3.141593
How to achieve this?
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 ... PI/4 = 1/1 - 1/3 + 1/5 - 1/7 + ...
const long double pi = acosl(-1.0L); printf("%. 20Lf\n", pi);
There are essentially 3 different methods to calculate pi to many decimals. One of the oldest is to use the power series expansion of atan(x) = x - x^3/3 + x^5/5 - ... together with formulas like pi = 16*atan(1/5) - 4*atan(1/239). This gives about 1.4 decimals per term.
The first 100 digits of pi are 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679. The value of pi starts with a 3 followed by a decimal point.
Using the R package bc (which is available at the foregoing link, not on CRAN):
> library(bc)
> bc("4 * a(1)", scale = 1000)
[1] "3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201988"
If you don't want to do the calculation yourself then you could look the number up. For example
pie <- read.csv("http://oeis.org/A000796/b000796.txt", header=FALSE, sep=" ")
dig <- 75 # up to 20000 digits
pistring <- paste(c(pie[1,]$V2, ".", head(pie[-1,], dig-1)$V2), collapse="")
would produce
> pistring
[1] "3.14159265358979323846264338327950288419716939937510582097494459230781640628"
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