# droplet_e: Droplet Algorithm for pi and e In numbers: Number-Theoretic Functions

## Description

Generates digits for pi resp. the Euler number e.

## Usage

 ```1 2``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```## 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) ```

### Example output

```[1] "2.71828182845904523536"
[1] 2.7182818284590450908
[1] "3.14159265358979323846"
[1] 3.141592653589793116

0   1   2   3   4   5   6   7   8   9
100  96  97 109 100  85  99  99 103 112

0   1   2   3   4   5   6   7   8   9
93 116 103 102  93  97  94  95 101 106
```

numbers documentation built on May 15, 2021, 1:08 a.m.