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Jangempo
Stranger
Registered: 01/08/03
Posts: 14
Loc: Canada
Last seen: 12 years, 8 months

base pi
#2429227  03/13/04 11:09 PM (13 years, 19 days ago) 


I was thinking about base number systems and how any number is supposed to be able to support it's own scale for mathematics.
My dad thought that 22/7 was close enough to pi, so I couldn't continue this conversation with him.
3 + 1/3  1/5 + 1/7  1/9 .... forever, is equal to pi. so, 3.14159... so, how can I use pi as a base?
between 0 and 3.14159... what are the increments between units? sure it doesn't go 0,1,2,3,3.14159...,4,5,6,6.282,7... it must be something crazy.
Wouldn't I need to use a different number system base to see how many units I wanted in between 0 and 3.14159 (our 10)?
What would be our 100? (in terms of positional units, not numerical value) 3.14159 3.14159's? It's just the base squared isnt it? a thousand is cubed, isn't it? 3.14159 * 3.14159 * 3.14159?
What other question should I be asking?

phi1618
old hand
Registered: 02/14/04
Posts: 4,102
Last seen: 6 years, 10 months


I am not a mathematician, but:
for number systems in which "base" is meaningful (i'm not sure that Roman numerals, for example, really have a base) base refers to the number of distinct symbols, and so can only have a positive integer value. for example, base ten allows ten distinct symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 base two allows 2 symbols: 0, 1 and base 1 allows 1 symbol: 1
The symbols themselves are unimportant, so i could express 5 in base 1 like this: LSD LSD LSD LSD LSD or in base 2 like this: LSD shrooms LSD, where shrooms = 0 and LSD = 1
So, you can't really have a noninteger number of different symbols.
Using the typical definition of a base, counting in base pi would be: 1 2 3 10, with (as you noted) 3  2 > 10  3. This is pretty inconvenient.
If you had a special reason to count in fractions of pi, you could apply pi as a scalar to some other base. For example, count in base 10, and set 1 = pi/10, so that 10 = pi. Basically, to convert from this system to base 10, just multiply by pi/10.
In any case, i don't think "any number is supposed to be able to support it's own scale for mathematics" in the sense you mean: I think only positive integer bases are useful or meaningful.
 


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