[comp.lang.c] 0.1

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
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BITNET: rice%cs.swarthmore.edu@swarthmr.bitnet
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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.