From: Thorsten Hater <th@...1.rub.de>
Date: 2010-01-11T22:57:39+09:00
Subject: Re: [QUIZ] Digits of e (#226)

Hello,

based on the spigot algorithm of Rabonitz and Wagon [1]:

#!/usr/bin/ruby

def spigot n
   e = []
   arr = [2] + Array.new(n+1,1)
   (n-1).times do |i|
     (n+1).downto 0 do |j|
       arr[j] *= 10
     end
     q = 0
     (n+1).downto 0 do |j|
       arr[j] += q
       q = arr[j]/(j+1)
       arr[j] %= j+1
     end
     e << q
   end
   e[0]/= 10.0
   puts e.join('')
end

if $0 == __FILE__
   spigot ARGV[0].to_i
end

[1] http://www.mathpropress.com/stan/bibliography/spigot.pdf : citing 
the easier case of e

Am 08.01.2010 06:26, schrieb Daniel Moore:
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> ## Digits of e (#226)
>
> Wayumbe Rubyists,
>
> The mathematical constant e is the unique real number such that the
> value of the derivative (slope of the tangent line) of the function
> f(x) = e^x at the point x = 0 is exactly 1. The function e^x so
> defined is called the exponential function, and its inverse is the
> natural logarithm, or logarithm to base e.[1]
>
> e is one of the most important numbers in mathematics, alongside the
> additive and multiplicative identities 0 and 1, the constant �, and
> the imaginary unit i. These are the five constants appearing in one
> formulation of [Euler's identity][2].
>
> This week�s quiz is to write a Ruby program that can compute the first
> 100,000 digits of e.
>
> Have fun!
>
> [1]: http://en.wikipedia.org/wiki/E_(mathematical_constant)
> [2]: http://en.wikipedia.org/wiki/Euler's_identity
>
>    


-- 
Thorsten Hater
Institut fuer Theoretische Physik I
Ruhr-Universitaet Bochum
E-Mail: tp1@tp1.rub.de
Tel.: 0234/32-23-441