Talk:Balanced ternary

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Are there balanced systems for any base other than three? I think there would be a requirement for the base to be odd, but other than that, why not balanced base 5? Balanced base 11 could be counted on the fingers, with one hand representing negative numbers and the other positive. Linguofreak 02:13, 19 March 2006 (UTC)

Yes, there are ballanced systems with digits other than three. An for the really preverse, there are workable systems with negative and positive digits that aren't balanced for even bases. (But this drifts off into original research, many people have played with them, nobody seems to have officially published.) Nahaj 11:46, 17 April 2006 (UTC)

Even bases, how does that work? I shall have to play around with this too. Linguofreak 02:28, 18 April 2006 (UTC)

Actually, I've been doing some OR in this myself (developed balanced ternary on my own about 15 years ago, though I called it "nullcentric trinary" back then, for obvious reasons), and it seems that 0 can occupy any position at all within the choice of digits; e.g., you could have an octal system that starts at -2, and goes up to 5 (though why you'd want to is beyond me). I haven't even ruled out systems that don't include 0, e.g. octal from 3 to (decimal) 10, but only because I haven't considered them yet. --John Owens | (talk) 18:10, 16 February 2007 (UTC)

Contents 1 Fudge Dice? 2 Abhijit Bhattacharjee's work appears to be original research 3 Use as currency 4 rounding 5 Evenness test 6 LeRoy Eide's algorithm

[edit] Fudge Dice?

I think someone should mention that one Fudge Die can produce one digit in balanced ternary. I'm not sure how to introduce this into either article.

[edit] Abhijit Bhattacharjee's work appears to be original research

Abhijit Bhattacharjee's work appears to be original research which has not yet been peer reviewed. It appears to be correct but I am not a mathematician so in line with policy I have added a template

Looking at the web page, I wouldn't exactly call it original. The system he describes for representing non-integer numbers is just the normal one: digits to the right of the decimal point get multiplied by successively smaller powers of the base (in this case, 1/3, 1/9, 1/27...). The description is longwinded, but that's all it boils down to. Carl Muckenhoupt 18:15, 25 October 2006 (UTC)

No, there is a crucial difference when it comes to fractional numbers as it has been pointed out in that work. For fractional numbers, you have to approach it from two directions, for those below .5 and for those above .5. Hence there is an inventive step. Just carrying on with ternary numbers wouldnt work because even if you add up all the ternary fractions it would not add up to more that .5

Don't we accept self published non peer-reviewed stuff from well published and recognised authors to some degree anyway? See Wikipedia:Reliable_sources#Self-published_sources. I'm not sure of coruse if this stuff was self-published Nil Einne 19:10, 26 October 2006 (UTC)

For fractional numbers, you have to approach it from two directions, just like balanced ternary, where you have to approach 26 from two directions: +00- = 1*3^3 + -1. There is no inventive step here. This is just carrying on with balanced ternary numbers. I am a high school junior, and this is completely obvious to me. --Zarel 21:03, 24 November 2006 (UTC)

Let me explain: Just like 9.0/10 is the same as 0.90 in decimal, 11.0/10 is the same as 1.10 in balanced ternary. All you're doing is moving the decimal place one to the left to divide by 10. I've edited the article accordingly. --Zarel 21:27, 24 November 2006 (UTC)

I am Abhijit Bhattacharjee and it wouldnt be possible for me to restore the page after each vandalisation. Just in case anyone cares, the page can be found here. http://www.abhijit.info/tristate/tristate.html where I have belaboured enough about its need and existence. —The preceding unsigned comment was added by 59.93.246.74 (talk • contribs) 03:10, 3 December 2006 (UTC).

[edit] Use as currency

Has the suggestion to use balanced tertiary for currency considered that it would be difficult to have people willingly keep things with negative value?-- unsigned edit by user:72.144.117.150 at 07:55, 28 October 2006

Read again... that's not what is suggested. But I guess it could be stated more clearly. The idea is really to use regular ternary coin sizes (1, 3, 9, 27), as that would minimize the number of coins to be exchanged, assuming both parties in the deal have a good supply of different coins.--Niels Ø 13:14, 28 October 2006 (UTC)

I have just reverted an addition along the same lines.--Niels Ø 16:48, 22 November 2006 (UTC)

I remember encountering coins with values of 3 and 15 in the Soviet Union, shortly before it ceased to exist. Does anyone have accurate info on these coins; is it covered anywhere in the wikipedia; is it (at least marginally) relevant here; is there a good way to include it?--Niels Ø 16:48, 22 November 2006 (UTC)

[edit] rounding

From the Article (text in italics recently added):

Donald Knuth has pointed out that truncation and rounding are the same operation in balanced ternary—they produce exactly the same result. Moreover, there is no ambiguity in rounding (a property shared with other odd bases) since the number half is not representable.

Isn't it because there is no representation for 0.5 (mid point) that truncation is the same as rounding. -- Chris Q 15:22, 8 December 2006 (UTC)

[edit] Evenness test

The article states, "The quick test for even is the analog of the base ten divide-by-nine test: add up all the digits and repeat until you have a one-digit number; the number is even if the final sum is zero."

It can be stated much more simply than that. A number is even if it has an even number of nonzero digits. (In general, in any odd base, balanced or ordinary, a number is even if it has an even number of odd digits.)

I'm not sure whether this should be given as an alternative method or whether it should replace the existing one. The general "odd base evenness test" and the "one less than base" division test coincide, making them both reasonable ways to approach the problem. However, I don't feel that the evenness test deserves too much text devoted to it, so if nobody says anything then (provided I don't forget!) I will replace the complicated method with the simple one. MarkC77 02:09, 9 December 2006 (UTC)

[edit] LeRoy Eide's algorithm

Does anyone know what LeRoy Eide's algorithm (mentioned in main article) is? Ian S 14:19, 27 March 2007 (UTC)