rob@kaa.eng.ohio-state.edu (Rob Carriere) (10/14/88)
In article <13983@mimsy.UUCP> chris@mimsy.UUCP (Chris Torek) writes: >If you want to get *really* ridiculous, 0.1 is irrational in irrational >bases, but I am not sure those count :-) . You lost me. How do you do a basis that is not a natural? Rob Carriere
rice@cs.swarthmore.edu (Dan Rice) (10/16/88)
In article <13983@mimsy.UUCP> chris@mimsy.UUCP (Chris Torek) writes: >If you want to get *really* ridiculous, 0.1 is irrational in irrational >bases, but I am not sure those count :-) . But Tom Neff is right (and >I missed that error in my first followup). >-- >In-Real-Life: Chris Torek, Univ of MD Comp Sci Dept (+1 301 454 7163) >Domain: chris@mimsy.umd.edu Path: uunet!mimsy!chris 0.1 may have a non-repeating representation in some irrational bases, but it is certainly rational regardless of how one chooses to write it... -- - Dan Rice, Swarthmore College, Swarthmore PA 19081 UUCP: ...!seismo!bpa!swatsun!rice, ...!sun!liberty!swatsun!rice BITNET: rice%cs.swarthmore.edu@swarthmr.bitnet CSNET: rice@cs.swarthmore.edu
chris@mimsy.UUCP (Chris Torek) (10/16/88)
>In article <13983@mimsy.UUCP> I suggested that >>If you want to get *really* ridiculous, 0.1 is irrational in irrational >>bases, but I am not sure those count :-) . In article <800@accelerator> rob@kaa.eng.ohio-state.edu (Rob Carriere) asks: >You lost me. How do you do a basis that is not a natural? Negative integer bases are easy: 111 base -2 = 1 (-2)^2 + 1 (-2)^1 + 1 (-2)^0 = 4 + -2 + 1 = 3 Positive or negative noninteger bases follow the same formula, but I must admit that inventing a notation for writing fractional digits is beyond me: 102 base pi = 1 pi^2 + 0 pi^1 + 1 pi^0 = pi^2 + 0 + 1 ~=~ 10.86960440108935861883449 I have no idea whether fractional and irrational bases are well-regarded in mathematical circles (mathematical circles are the ones that are *really* round, rather than the merely arbitrary polygonal CS circles :-) ). -- In-Real-Life: Chris Torek, Univ of MD Comp Sci Dept (+1 301 454 7163) Domain: chris@mimsy.umd.edu Path: uunet!mimsy!chris
dik@cwi.nl (Dik T. Winter) (10/17/88)
In article <14014@mimsy.UUCP> chris@mimsy.UUCP (Chris Torek) writes: > In article <800@accelerator> rob@kaa.eng.ohio-state.edu (Rob Carriere) asks: > >You lost me. How do you do a basis that is not a natural? > ... > > I have no idea whether fractional and irrational bases are well-regarded > in mathematical circles (mathematical circles are the ones that are *really* > round, rather than the merely arbitrary polygonal CS circles :-) ). > -- You might check Knuth vol. 2, which details base 2i and i-1. If that isn't irrational. -- dik t. winter, cwi, amsterdam, nederland INTERNET : dik@cwi.nl BITNET/EARN: dik@mcvax
rob@raksha.eng.ohio-state.edu (Rob Carriere) (10/17/88)
In article <14014@mimsy.UUCP> chris@mimsy.UUCP (Chris Torek) writes: > [...] >I must admit that inventing a notation for writing fractional digits >is beyond me: [...] That's where you lost me. In base b we have b different digits, so in base e we have .... well, eh, we should have... that is to say, ... >I have no idea whether fractional and irrational bases are well-regarded >in mathematical circles (mathematical circles are the ones that are *really* >round, rather than the merely arbitrary polygonal CS circles :-) ). That's OK, engineering circles are just plain irregular :-) Rob Carriere
cwitty@csli.STANFORD.EDU (Carl Witty) (10/18/88)
In article <821@accelerator> rob@raksha.eng.ohio-state.edu (Rob Carriere) writes: >In article <14014@mimsy.UUCP> chris@mimsy.UUCP (Chris Torek) writes: >> [...] >>I must admit that inventing a notation for writing fractional digits >>is beyond me: [...] > >That's where you lost me. In base b we have b different digits, so in >base e we have .... well, eh, we should have... that is to say, ... > >>I have no idea whether fractional and irrational bases are well-regarded >>in mathematical circles (mathematical circles are the ones that are *really* >>round, rather than the merely arbitrary polygonal CS circles :-) ). > >That's OK, engineering circles are just plain irregular :-) > >Rob Carriere I'm not sure where I read about this...perhaps in one of Martin Gardner's Scientific American columns? The positive root of x*x = x+1 makes an interesting number base. This is the Golden Ratio, (1 + sqr(5))/2, or about 1.618. It's interesting because the above equation shows that the patterns "011" and "100" are interchangeable, anywhere in a number. e.g. 111 = 1001 and 1.011 = 1.1. This makes for interesting addition--for example, 111+111 = 1001+111 = 1001+110+1 = 1111+1 = 10011+1 = 10100+1 = 10101 . -- Carl Witty Internet: cwitty@csli.Stanford.EDU
flaps@dgp.toronto.edu (Alan J Rosenthal) (10/19/88)
In article <7668@boring.cwi.nl> dik@cwi.nl (Dik T. Winter) writes: >You might check Knuth vol. 2, which details base 2i and i-1. If that isn't >irrational. ??? Of course those numbers aren't irrational. They're complex.