Wikipedia:Reference desk/Archives/Mathematics/2012 January 22

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January 22

PI on Base n

is there any research about computing pi in other bases? im no math expert and i dont really know how other bases work, i just read somewhere about something with base 13, so i dont know if my question makes sense or not. MahAdik _usap 00:01, 22 January 2012 (UTC)

Yes there is a lot of research in that. The most well known result is probably the Bailey–Borwein–Plouffe formula which can be used to compute any binary digit of pi without computing all the previous digits. Computing digits of pi in base 10 typically can't be done in this way- if you want the millionth digit, you have to compute all of the first million digits. Not so in binary (which is base 2)- you can compute whatever digit you like by itself without doing any other computations. Staecker (talk) 00:18, 22 January 2012 (UTC)

Thats cool, im glad i asked that question. Is there any application for that formula? and actually my goal for that question is i know pi doesnt repeat its digits, im wondering if its the same case in other bases. MahAdik _usap 00:37, 22 January 2012 (UTC)

It definitely doesn't repeat in other bases; that would make it a rational number, and much as in base ten repeating decimals are associated with rational numbers.--JohnBlackburne^words_deeds 00:45, 22 January 2012 (UTC)

(Of course 'repeating decimal' should be replaced with whatever's appropriate in the base under consideration - the point is the arithmetic of e.g. converting repeating decimals to fractions can be done in any base)--JohnBlackburne^words_deeds 00:51, 22 January 2012 (UTC)

The OP may also be interest in Pi#Open questions, particularly the paragraph about normality, as it involves pi in other bases. -- ToE 10:23, 22 January 2012 (UTC)

On a different note, base $2$ and by consequence, base $2^{n}$, has the peculiarity that one can compute directly and quickly the N-th digit without computing the preceding ones. So for instance the $\scriptstyle 4\cdot 10^{13}$-th binary digit of $\pi$ is known to be $0.$ This is made possible by the BBP formula (an analogous formula that works for other bases is not known). --pma 15:48, 22 January 2012 (UTC)

Proving a chord to be diameter

Is it possible to prove in the following figure that BD is a diameter?[1] Srinivas 05:53, 22 January 2012 (UTC)

No, if the only requirement is that BC = AM, then BD need not be a diameter. Rckrone (talk) 06:31, 22 January 2012 (UTC)

And what if AB=AC? Srinivas 08:20, 22 January 2012 (UTC)

Just try it with an equilateral triangle then D will be C and it is obvious BC is not a diameter. Dmcq (talk) 08:50, 22 January 2012 (UTC)

(edit conflict) Still not necessarily a diameter. Triangles ADM and BCM are similar, but making non-corresponding sides equal doesn't change much. You have to make AM equal to BM for congruence, but then M is the centre of course. Dbfirs 08:55, 22 January 2012 (UTC)

Alright, thank you sirs. Srinivas 09:38, 22 January 2012 (UTC)

t-test and Chi-squared Test

Hello. When is a Student's t-test preferred over the chi-squared test? My highest level of education in statistics is a high school introductory course; so please keep the explanation simple. Thanks in advance. --Mayfare (talk) 16:06, 22 January 2012 (UTC)

Pearson's chi-squared test is for count data, Student's t-test for continuous measurements. HTH, Robinh (talk) 20:13, 22 January 2012 (UTC)