Talk:81 (number)

Link for -20
I don't think the link to -20 is what this article wants. Check to see if it is correct. Georgia guy 00:51, 31 Jan 2005 (UTC)

I just heard an unconfirmed report that a new number has been discovered between 80 and 81. If true, this could have major implications for number 81. —Preceding unsigned comment added by Kackermann (talk • contribs) 14:31, 21 October 2007 (UTC)

Specific and general
That $$\frac{1}{81}$$ exhibits the sequence of digits except 8 is just the base-10 case of the general rule that $$\frac{1}{(n-1)^2}$$ for any base n gives the sequences of digits except n−2. Cf. $$\frac{1}{121}$$ in base 12, $$\frac{1}{225}$$ in base 16 (0.0123456789ABCDF…) to name just two. --109.67.200.119 (talk) 16:13, 10 June 2010 (UTC)
 * I think you're right. Perhaps we should say that in the article.  In fact, I will.  — Arthur Rubin  (talk) 17:09, 10 June 2010 (UTC)
 * Thanks. It's of high probability I'm right, because I tested this on a great number of bases using bc, and they all bear it out. However, as with trying out a million triangles of two equal edges and one equal angle and finding out they overlap, that only makes for high probability, not mathematical proof. I don't know a proof. --109.67.200.119 (talk) 17:35, 10 June 2010 (UTC)


 * Let me see....(I don't know how to do alignments in TeX.)
 * $$123\ldots(b-4)(b-3)(b-1)_b=1+\sum_{k=0}^{b-2} b^k (b-2-k)$$
 * $$=1+\sum_{l=0}^{b-3}\sum_{k=0}^l b^k$$
 * $$=1+\sum_{l=0}^{b-3} \frac {b^{l+1}-1}{b-1}$$
 * $$=1-\frac{b-2}{b-1}+\frac{1}{b-1}\sum_{l=0}^{b-3} b^{l+1}$$
 * $$=\frac{1}{b-1}+\frac{1}{b-1}\sum_{l=0}^{b-3} b^{l+1}$$
 * $$=\frac{1}{b-1}\sum_{l=0}^{b-2} b^l$$
 * $$=\frac{b^{b-1}-1}{(b-1)^2}.$$

(Informative) Also applies to signed-digit bases. $$\frac{1}{676}$$ (676 = square of 26) in balanced base 27 (which stands for three balanced ternary digits much like hexadecimal stands for four binary digits): $$0.0123456789ABD\overline{DCBA987654321}0123...$$ (the vinculum marks the negative digits). --79.178.202.78 (talk) 17:06, 26 July 2010 (UTC)

It is also the only number…
Where the sum of its digits equal its square root. Is anyone going to revert this if I make an article change? —Preceding unsigned comment added by Da5id403 (talk • contribs) 23:48, 12 May 2011 (UTC)

Hell's Angels
81 is also the number for the Hells Angels MC. 8=H 1=A — Preceding unsigned comment added by 71.231.251.27 (talk) 16:37, 8 September 2014 (UTC)

Bingo names -
Please see Wikipedia talk:WikiProject Numbers for a centralized discusion as to whether Bingo names should be included in thiese articles. Arthur Rubin (alternate) (talk) 23:35, 3 June 2018 (UTC)