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One could sort of satisfy naturalethic's wish by choosing a numeral system with pi as basis. Then pi would have digit representation '1' in this system. And yes

One could sort of satisfy naturalethic's wish by choosing a numeral system with pi as basis. Then pi would have digit representation '1' in this system. And yes, mathematicians have studied transcendental bases for numeral systems (Knuth in particular, see the short paragraph on http://mathworld.wolfram.com/Base.html http://mathworld.wolfram.com/Base.html which explicitly mentions pi as basis). Of course it's not a good idea to base your day-to-day numeral system on pi, but I know that at least for irrational bases there are actual applications.

mej10 14y ago
This is a good point as well, and more in line with what the original commenter was asking. Using pi as a base is even briefly discussed on wikipedia. I had some interest in using e as the basis for a while, since (as is pointed out on wiki) "The base e is the most economical choice of radix β > 1 (Hayes 2001), where the radix economy is measured as the product of the radix and the length of the string of symbols needed to express a given range of values." http://en.wikipedia.org/wiki/Non-integer_representation#Examples http://en.wikipedia.org/wiki/Non-integer_representation#Exam...
jerf 14y ago
"One could sort of satisfy naturalethic's wish by choosing a numeral system with pi as basis. Then pi would have digit representation '1' in this system." I'm pretty sure pi comes out to 10 base pi, not 1 base pi.
- anonymouz 14y ago
  Ah, right, of course! Still, I think this is the closest possible to the wish the OP had.
- blacksmythe 14y ago
  Numeral systems are not restricted to the set (base N). "a numeral system with pi as basis" could be (base pi)pi, where pi =-> '1' and pipi -> '10' and unity -> '0.1'.
  - jerf 14y ago
    I'd refer you back to philh's answer. You can do that and it isn't "wrong", but it is surprisingly uninteresting, as compared to a discussion of irrational or negative or imaginary bases.

mej10 14y ago

This is a good point as well, and more in line with what the original commenter was asking. Using pi as a base is even briefly discussed on wikipedia. I had some interest in using e as the basis for a while, since (as is pointed out on wiki) "The base e is the most economical choice of radix β > 1 (Hayes 2001), where the radix economy is measured as the product of the radix and the length of the string of symbols needed to express a given range of values." http://en.wikipedia.org/wiki/Non-integer_representation#Examples http://en.wikipedia.org/wiki/Non-integer_representation#Exam...

jerf 14y ago

"One could sort of satisfy naturalethic's wish by choosing a numeral system with pi as basis. Then pi would have digit representation '1' in this system." I'm pretty sure pi comes out to 10 base pi, not 1 base pi.

anonymouz 14y ago
Ah, right, of course! Still, I think this is the closest possible to the wish the OP had.
blacksmythe 14y ago
Numeral systems are not restricted to the set (base N). "a numeral system with pi as basis" could be (base pi)pi, where pi =-> '1' and pipi -> '10' and unity -> '0.1'.
- jerf 14y ago
  I'd refer you back to philh's answer. You can do that and it isn't "wrong", but it is surprisingly uninteresting, as compared to a discussion of irrational or negative or imaginary bases.