numbers (version 0.5-6)

dropletPi: 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.

Value

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

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 socalled "radix conversion".

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

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