0.1

[Carl Witty]

In article <821 at accelerator> rob at raksha.eng.ohio-state.edu (Rob Carriere) writes:
>In article <14014 at mimsy.UUCP> chris at 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 at csli.Stanford.EDU