September 2011 - mathfun@mailman.xmission.com

Re: [math-fun] somewhat related to "words for really long numbers
by Phil Carmody 12 Oct '11

12 Oct '11

Bill Gosper <billgosper(a)gmail.com>: > Yeah, what about 2*10^4679+3, (two zillion and three)-? It seems to precede 2*10^4772+2003 (two zillion two thousand and three) Phil -- [aside - I'm very pro- correct email usage, but use the digest so can't reply (header-wise) to a real post; I always try to manually get the subject line correct - does this mess up people's threading?]

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[math-fun] Machine Go
by rcs＠xmission.com 12 Oct '11

12 Oct '11

Science Daily has a report of a recent success for a Go program. http://www.sciencedaily.com/releases/2009/05/090514083931.htm The program Huygens defeated two professional Go players. The program had handicaps of 6 or 7 stones. Question for the Go players among us: Does a handicap of 6 stones mean that the starting board has 6 stones added for the weaker player, or that 6 is added to the final score? Rich

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[math-fun] Update on IMO/RKG-inspired conics thru' 6 points of triangle
by Fred lunnon 03 Oct '11

03 Oct '11

Notation: initial triangle T with corners P,Q,R; side lengths a,b,c; angles A,B,C; centre point S = (B_1 P + B_2 Q + B_3 R)/(B_1+B_2+B_3), where homogeneous barycentric coordinates B are some function of T; 3 cevian points PS.QR = U,V,W; 6 subsidiary triangles SPU etc. The 6 subsidiary centres appear to lie on a conic, for (all) triangle centres lying at the (1) centroid, B = [1,1,1]; (2) incentre, B = [a,b,c] or [sin A, ... ]; (3) e-centres, B = [-a,b,c], etc --- reliant on vertex ordering!; (4) circumcentre, B = [a^2(b^2+c^2-a^2), ... ] or [sin 2A, ... ]; (5) orthocentre B = [1/(b^2+c^2-a^2), ... ] or [tan A, ... ]; (6) first isogenic point X13, B = [a sec(A - pi/6), ... ]; In general (non-isosceles) they fail to lie on a conic for (7) symmedian point B = [a^2,b^2,c^2 or 1 - cos 2A, ... ]; (8) second isogenic point X14, B = [a sec(A + pi/6), ... ]; (9) fixed weight with B general constant vector (correcting earlier claim). The conjectures are based on evaluating the 6x6 determinant of quadratic monomials in the (projective) coordinate components. Fermat points (6),(7) cause particular difficulty, with the determinant evaluated only approximately: for example WFL's {12,17,25}-sided test triangle required at least 70 decimal-digit precision to confirm case (6), and case (7) was rejected with determinant ~ -2.538 E-13 . Fred Lunnon

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[math-fun] psycho-history, etc
by Simon Plouffe 30 Sep '11

30 Sep '11

Hello, there are 2 recent news that are worth looking at : http://singularityhub.com/2011/08/29/pre-cog-is-real-%E2%80%93-new-software… http://singularityhub.com/2011/09/25/supercomputer-predicts-revolution/ This reminds me of that old idea of Isaac Asimov about psycho-history that everybody found kind of way out at the time (including me)!, This means that with enough computer juice and a suitable set of data, like hundreds of millions of articles an heuristic program can predict 'something'. A good question is, they had this Watson machine capable of answering a general question, then this engine that can predict a political movement and that later one that can predict human behaviour, then what's next ?? Best regards, Simon Plouffe

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Re: [math-fun] somewhat related to "words for really long numbers
by Dan Asimov 30 Sep '11

30 Sep '11

Hmm, what about umpteen zillion? --Dan Hans wrote: << . . . So, let's prepend the 'two zillion' (2*10^n) and force the presumably- optimal 23 ending. 2*10^n (two zillion) +2*10^63 (two vigintillion) +2*10^36 (two undecillion) +2*10^12 (two trillion) +2000 (two thousand) +200 (two hundred) +20 (twenty) +3 (three) . . . >> Sometimes the brain has a mind of its own.

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[math-fun] garbled ellipse length
by Bill Gosper 28 Sep '11

28 Sep '11

The Wikipedia ellipse article borrows (with the Goldwynism "For computational purposes a much faster series where the denominators vanish at a rate ...") a series from http://www.iamned.com/math/ which offers "A Rapidly converging formula for the circumference of an elipse that gives log (1024/27((a+b)/(a-b))^8) digits per term : ", a formula satisfyingly symmetrical in a and b, but which unfortunately vanishes (instead of 4a) for b=0, and generally fails for b<a. Does anybody know what this should be? The Wikipedia article actually corrects an obvious asymmetry in the iamned.com source, but the Wikigrapher must not have tested it. --rwg Here is what I typed: 8*\[Pi]/Q^(5/4)* Sum[Pochhammer[1/12, n]*Pochhammer[5/12, n]*(v1 + v2*n)* r^n/n!^2, {n, 0, \[Infinity]}] /. r -> 432*(a^2 - b^2)^2*(a - b)^6*b*a/Q^3 /. Q -> b^4 + 60*a*b^3 + 134*a^2*b^2 + 60*a^3*b + a^4 /. v1 -> a*b*(15*b^4 + 68*a*b^3 + 90*a^2*b^2 + 68*a^3*b + 15*a^4) /. v2 -> -a^6 - b^6 + 126*(a*b^5 + b*a^5) + 1041*(a^2*b^4 + a^4*b^2) + 1764*a^3*b^3 A correct formula for a>=b is elliplen[a_, b_] := 4*a*EllipticE[Sqrt[1 - b^2/a^2]]

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Re: [math-fun] garbled ellipse length
by rcs＠xmission.com 28 Sep '11

28 Sep '11

I'm having trouble parsing the EllipticE infinite series formula. Could you clarify if the 432^N is in the numerator or denominator, and similarly for the other terms? I suspect I don't understand the grouping of terms in Mma. Rich ---- Quoting Bill Gosper <billgosper(a)gmail.com>: <clippage -- rcs> > This means that > EllipticE[1-r^2]==(2 \[Pi] Sum[-1/(n!)^2*432^n (((-1+r)^8 r (1+r)^2)/(1+60 > r+134 r^2+60 r^3+r^4)^3)^n (-r (15+68 r+90 r^2+68 r^3+15 r^4)+n (1-126 > r-1041 r^2-1764 r^3-1041 r^4-126 r^5+r^6)) Pochhammer[1/12,n] > Pochhammer[5/12,n],{n,0,\[Infinity]}])/(1+60 r+134 r^2+60 r^3+r^4)^(5/4) > > is an impressive acceleration formula for E'(r^2). > > You might be tempted to object that the k-fold speedup is cancelled by the > general term being k times more > complicated, but this is not the case. Once r is fixed, this is just a > matrix product over n of > > quadratic/quadratic linear > ( ). > 1 0 > > However, it does cost a factor of 2 if you are computing megadigits of > E'(nonsquare rational). > > A correct formula for a>=b is >>> elliplen[a_, b_] := 4*a*EllipticE[Sqrt[1 - b^2/a^2]] >>> >> >> No, elliplen[a_, b_] := 4*a*EllipticE[1 - b^2/a^2] >> --rwg >> > Which is, in fact, (nonobviously) symmetrical in a and b. > --rwg > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >

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[math-fun] How to speak long numbers -- now I'm really curious (-:
by Robert Munafo 28 Sep '11

28 Sep '11

I have found some folks over on math-fun who have encountered "and" when spelling out (or I guess speaking) names of numbers over 1000. Also a lot of disagreement to my claim that commas should be written in the same places where the comma would appear in the digits version. But no-one is giving specific rules (yet :-) and I've spent a while looking but haven't found any rules myself. (Just isolated examples without explanation) So here are some questions for our colleagues who speak the word "and" as part of a number name -- and regarding the comma, consider how you would write it out in words: * Do you ever or always use "and" after a power of 1000 if something else follows? ("one million and thirty thousand") * Do you ever or always use "and" in places where there would be a comma in the digits? ("five thousand three hundred forty seven" but "twelve thousand and three hundred forty seven") * Or instead of "and" would you put a comma in the words? ("twelve thousand, three hundred forty seven") * Do you use "and" wherever there are 0s between digits? ("one hundred and seven") * Do you do two or more of the above? ("five thousand and one hundred and one" or maybe "five thousand, one hundred and one") * Do you put "and" anywhere else? ("three hundred and forty seven") * Does it matter how many syllables the part after "and" has? ("one thousand and twelve" but "one thousand seventy-seven") * Other rules? * If you consider it proper usage in only part of the English speaking world (like the UK, Australia, Canada, U.S. etc.) let me know that too. It would be nice to formalize this, because it is used a lot, and almost everything else in OEIS never uses "and", and is mute on commas. I found 7 OEIS sequences where it is clear if they use "and" or not, there might be more... A005589 includes a PARI program which gives A005589(1000)=11 and A005589(1001)=14. A052360 has the same program. A052363 agrees with A005589 and A052360 because it includes 1103 but not 1077. A058230 specifically claims "not to put the word 'and' in the names of numbers" A092320 agrees because it contains 1005. A134629 uses Noll's program. [1] *but* A126259 uses "and" in its spelling of 108 - Robert Munafo [1] http://isthe.com/cgi-bin/number.cgi On Sun, Sep 25, 2011 at 13:33, Victor Miller <victorsmiller(a)gmail.com>wrote: > On the program cartalk last week, there was a puzzle of the following form: > A list of numbers was given, and one was asked what they had in common > (I give the actual puzzler at the end). The answer was that each of > these numbers was divisible by the number of letters (excluding > spaces) in the standard spelling out of the number in words. This got > me to thinking of the following modification: > [...] (there followed speculation about A092320 vs. A126259) > -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com

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Re: [math-fun] somewhat related to "words for really long numbers"
by Bill Gosper 28 Sep '11

28 Sep '11

>From: Robert Baillie <rjbaillie(a)frii.com <http://gosper.org/webmail/src/compose.php?send_to=rjbaillie%40frii.com>> >To: math-fun <math-fun(a)mailman.xmission.com <http://gosper.org/webmail/src/compose.php?send_to=math-fun%40mailman.xmissi…>>>Sent: Monday, September 26, 2011 4:24 PM>Subject: [math-fun] somewhat related to "words for really long numbers">>8,018,018,851 is the first prime number in alphabetical order (in english) (eight billion eighteen million eighteen thousand eight hundred fifty one)>>the last prime in alphabetical order is>2,000,000,000,000,000,000,000,000,002,000,000,000,000,000,000,000,002,000,000,002,293>(two vigintillion two undecillion two trillion two thousand two hundred ninety-three)>>see:>http://www.primepuzzles.net/puzzles/puzz_143.htm>_______________________________________________ ES>In order to justify the claim for the last prime, it seems necessary to have a naming algorithm that accepts all integers. Does such exist? -- Gene ------- Yeah, what about 2*10^4679+3, (two zillion and three)-? --rwg Mathematica 8.01 pronounces the "and" for 203, ..., 200003, but seems to say "two million n three", etc., and for 20000000003, "Approximately two point zero failed power".

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Re: [math-fun] How to speak long numbers -- now I'm really curious(-:
by Tom Karzes 27 Sep '11

27 Sep '11

Here's the first reference that I found: http://esl.about.com/library/beginnercourse/bl_beginner_course_numberbasic.… I didn't look further than that and the wiki page. For what it's worth, I like the so-called American style, both because I'm used to it and because it seems cleaner to me. When writing out lists of items, on the other hand, I have a preference for using the "Oxford Comma", also known as the "Harvard Comma". For instance, I will write: I like apples, bananas, and oranges. (The comma before the "and" is the one in question.) The reason I like it is because it most closely matches the pauses I insert when speaking aloud. It also avoid some ambiguous cases. Tom Dan Asimov writes: > I was taught the same thing. > > But Wikipedia is a very unreliable reference when it comes to > proper word usage. In fact it is almost universally agreed by > experts (unfortunately) that either method is correct in the U.S. > It's generally considered an issue of style rather than correct > spelling. > > --Dan > > << > I was taught not to use "and" in the integer portion of a number when > spelling it out, nor to use commas. A quick web check confirmed you > should not use "and" for American spelling, but that you should use it for > the hundreds portion in British spelling. Example: "seven hundred > twenty-seven" (American) vs. "seven hundred and twenty-seven" (British). > > Here's a reference: > > http://en.wikipedia.org/wiki/American_and_British_English_differences#Numbe… >>> > > Sometimes the brain has a mind of its own. > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > >

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