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Posers and Puzzles

slatington, pa, usa

Joined 28 Dec '04 Moves 52724 Bases don't have to be rational.

Joined 21 Feb '06 Moves 6830 Originally posted by sonhouse
Bases don't have to be rational. Surely you can only use the digits 0, 1, 2 and 3 in base pi?

In the den

Joined 09 Jun '07 Moves 45641 If it has a meaning
pi^4 + 3pi^3 + 6pi^2 + 7pi + 6/pi
I suppose?!?!?

Joined 21 Feb '06 Moves 6830 Originally posted by wolfgang59
If it has a meaning
pi^4 + 3pi^3 + 6pi^2 + 7pi + 6/pi
I suppose?!?!? No, it would be pi^3 + 3.pi^2 + 6.pi + 7 + 6/pi

slatington, pa, usa

Joined 28 Dec '04 Moves 52724 Originally posted by Fat Lady
Surely you can only use the digits 0, 1, 2 and 3 in base pi? I was lying down going to sleep and I realized I shouldn't use so many digits, was thinking about binary, 0 and 1, octal, 0-8 and so forth so it must be only 0,1,2,3 for PI. So what would 1223.22 be in PI?

Joined 31 May '07 Moves 696 1223.22 in base pi
is
pi^3 + 2pi^2 + 2pi + 3 + 2/pi + 2/(pi^2) in base 10
I think it's better leaving it in base pi.

In the den

Joined 09 Jun '07 Moves 45641 Originally posted by Fat Lady
No, it would be pi^3 + 3.pi^2 + 6.pi + 7 + 6/pi ðŸ˜³

the shame ................

Joined 11 Nov '05 Moves 43938 A arbitrarily chosen base, integer, rational, end even real bae, never done that, very interesting.
The formula goes: sum{a(i)*b^i}
where i is an integer from low to high,
and b is a real base > 1, I suppose?
It doesn't make sense if b < 0, and definitely not when b=1, correct?
Can we use the formula to construct any real number?