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OfflineJangempo
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Registered: 01/08/03
Posts: 14
Loc: Canada
Last seen: 13 years, 1 month
base pi
    #2429227 - 03/13/04 11:09 PM (13 years, 6 months 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?


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Offlinephi1618
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Registered: 02/14/04
Posts: 4,102
Last seen: 7 years, 4 months
Re: base pi [Re: Jangempo]
    #2439200 - 03/16/04 02:16 PM (13 years, 6 months ago)

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 non-integer 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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