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Number system with an irrational base 
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#1
Oct1710, 07:41 PM

P: 133

Could you provide a link to a 'number system with an irrational base'?
I only found this link http://www.jstor.org/pss/3029218 The link shows a small part of this number system ... I would to know more about it. 


#2
Oct1710, 08:17 PM

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There's not much to say  they work just like number systems with rational bases.



#3
Oct1710, 09:42 PM

P: 133

Actually, I'm interested in the unusual bases, such as,
 Base 1  Fibonacci base system  Irrational bases: pi base, e base, Phi base The Fibonacci base system is easy. Base 1 : I haven't looked into it, yet. Irrational bases  Bergman investigated irrational bases in 1957 [Bergman, G. "A Number System with an Irrational Base"] ... I don't have access to Bergman's article. Have you read it? base pi and base e not so common  they are impractical. phi is irrational and is solution to x^2  x  1 = 0 pi and e cannot be roots of a polynomial with integral cefficients. This statement caught my attention: Source: http://www.artofproblemsolving.com/R...s/FracBase.pdf 


#4
Oct1810, 08:25 AM

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Number system with an irrational base
For base 1, search for "unary"; you'll find a lot of things using it, though probably not too much discussing it directly (again, there's not much to say).
"Base efficiency" in that sense relates to expected length of representation times number of symbols (the persymbol entropy, really, when we look at noninteger bases). It's not hard to do the calculation on your own here. 


#5
Oct1810, 08:28 AM

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"Base 1" is easy: 1, 11, 111, 1111, 11111 are the numbers that, in base 10, would be called 1, 2, 3, 4, 5.



#6
Oct1810, 10:03 AM

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P: 2,892

Harmonic basis is funny:
0+ a/2! + c/3! + d/4! + e/5! + or something son. For each n, the coefficient must be an integer less than n. 


#7
Mar1712, 03:35 PM

P: 133

Has anyone explored base 3/2 ?
Write in base 3/2 the numbers 1, 2, 3,...,10, ... 20,... 


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