From: Thorsten Hater <th@...1.rub.de>
Date: 2010-01-11T22:59:48+09:00
Subject: Re: [QUIZ] Digits of e (#226)

Sorry, Rabonitz meant Rabinowitz, ugly typo.

Am 11.01.2010 14:57, schrieb Thorsten Hater:
> 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