dropletPi {numbers}

Droplet Algorithm for pi and e

Description

Generates digits for pi resp. the Euler number e.

Usage

dropletPi(n)
dropletE(n)

Arguments

n

number of digits after the decimal point; should not exceed 1000 much as otherwise it will be very slow.

Details

Based on a formula discovered by S. Rabinowitz and S. Wagon.

The droplet algorithm for pi uses the Euler transform of the alternating Leibniz series and the so-called “radix conversion".

Value

String containing “3.1415926..." resp. “2.718281828..." with n digits after the decimal point (i.e., internal decimal places).

References

Borwein, J., and K. Devlin (2009). The Computer as Crucible: An Introduction to Experimental Mathematics. A K Peters, Ltd.

Arndt, J., and Ch. Haenel (2000). Pi – Algorithmen, Computer, Arithmetik. Springer-Verlag, Berlin Heidelberg.

Examples

##  Example
dropletE(20)                    # [1] "2.71828182845904523536"
print(exp(1), digits=20)        # [1]  2.7182818284590450908

dropletPi(20)                   # [1] "3.14159265358979323846"
print(pi, digits=20)            # [1]  3.141592653589793116

## Not run: 
E <- dropletE(1000)
table(strsplit(substring(E, 3, 1002), ""))
#    0   1   2   3   4   5   6   7   8   9 
#  100  96  97 109 100  85  99  99 103 112

Pi <- dropletPi(1000)
table(strsplit(substring(Pi, 3, 1002), ""))
#   0   1   2   3   4   5   6   7   8   9 
#  93 116 103 102  93  97  94  95 101 106 
## End(Not run)