March 2005 - mathfun@mailman.xmission.com

[math-fun] Sliding numbers
by Eric Angelini 09 Mar '05

09 Mar '05

Hello SeqFan and Math-fun, Let's start with an example of "sliding number": 1/4 + 1/25 = 0.29 --> 29 is a "sliding number" 1/8 + 1/125 = 0.133 --> 133 is a "sliding number" 1/2 + 1/5 = 0.7 --> 7 is a "sliding number" etc. Note that : 1/20 + 1/50 = 0.70 --> 70 is a "sliding number" though 0.70 is usually written 0.7 So any "sliding number" G produces an infinite quantity of others : Gx10, Gx100, Gx1000, etc. Generally speaking we have this: 1/a + 1/b = (a+b)/10^k [with k=1,=2,=3,=4, ...] --> the "sliding number" G = a+b My pb is to build a correct seq. of G's (how not to forget any G behind?) By hand I've proceeded so: 10 --> 1+10 --> G(2)=11 2+5 --> G(1)=7 100 --> 1+100 --> G(7)=101 2+50 --> G(6)=52 4+25 --> G(5)=29 5+20 --> G(4)=25 10+10 --> G(3)=20 1000 --> 1+1000 --> G(15)=1001 2+500 --> G(14)502 4+250 --> G(13)=254 5+200 --> G(12)=205 8+125 --> G(11)133 10+100 --> G(10)=110 20+50 --> G(9)=70 25+40 --> G(8)=65 ... but you see now my pb: G(8) and G(9) are < G(7) ! I have to rename them... The sequence would then start like this: 7,11,20,25,29,52,65,70,101,110,133,205... BUT: 10000 --> 100+100 (among others) which gives G=200... So I have to correct the sequence and insert 200: 7,11,20,25,29,52,65,70,101,110,133,200,205... [BTW 200 is G(3)x10] Could someone compute enough terms to be submitted to the OEIS without leaving any G integer behind? Many thanks, É. ----------- PS. I don't know who has given the name "sliding numbers" to those integers -- I might have read that on the Internet somewhere around 1997...

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[math-fun] Penguin Dictionary of Curious and Interesting Geometry
by Daniel Asimov 08 Mar '05

08 Mar '05

Do people know this book, "The Penguin Dictionary of Curious and Interesting Geometry" by David Wells (1992)? I just chanced on it on my shelf of Long Lost Books, and find that it bears many repeated browsings. It has a number of old chestnuts, but also a huge number of geometric tidbits (and a few topological ones) that I hadn't seen before or knew very little about. It's written engagingly and pretty clearly, and has excellent B&W graphics to accompany each little squib. For example, the 6 circles theorem: Given a triangle in the plane, draw a circle tangent to just a pair of its sides. Now pick a different pair of sides, and draw the unique circle tangent to those sides and the first circle. Now there will always be a unique new circle if you keep choosing the pair of sides not used for the last 2 circles and repeat this operation. Theorem: After six circles are drawn this way, the seventh is the first, the eighth is the second, etc. (David Wells also wrote the "Penguin Dictionary of Curious and Interesting Numbers", which I've heard is also good.) Dan

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Re: [math-fun] Mathematics as punishment in the New Testament
by Daniel Asimov 08 Mar '05

08 Mar '05

Henry Baker asks: << Did they commute his sentence? Come on, Henry, you know quaternions don't commute. --Dan -------------------------------------------------- At 07:43 PM 3/7/2005, Mike Stay wrote: >1 NOW about that time Herod the king stretched forth his >hands to vex certain of the church. > >2 And he killed James the brother of John with the sword. > >3 And because he saw it pleased the Jews, he proceeded >further to take Peter also. (Then were the days of >unleavened bread.) > >4 And when he had apprehended him, he put him in prison, and >delivered him to four quaternions... >>

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Re: [math-fun] New Mersenne Prime
by David Wilson 08 Mar '05

08 Mar '05

Guess I got the previous one. ----- Original Message ----- From: "Meeussen Wouter (bkarnd)" <wouter.meeussen(a)vandemoortele.com> To: <ham>; <davidwwilson(a)comcast.net> Sent: Tuesday, March 08, 2005 1:32 PM Subject: RE: [math-fun] New Mersenne Prime the recently discovered Mersenne Prime is -1+2^25964951 You surely meant that one? W.

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[math-fun] Mathematics as punishment in the New Testament
by Mike Stay 08 Mar '05

08 Mar '05

1 NOW about that time Herod the king stretched forth his hands to vex certain of the church. 2 And he killed James the brother of John with the sword. 3 And because he saw it pleased the Jews, he proceeded further to take Peter also. (Then were the days of unleavened bread.) 4 And when he had apprehended him, he put him in prison, and delivered him to four quaternions... (KJV Acts 12:1-4) -- Mike Stay staym(a)clear.net.nz http://www.cs.auckland.ac.nz/~msta039

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[math-fun] New Mersenne Prime
by David Wilson 08 Mar '05

08 Mar '05

I remember as a youth reading about the largest known prime in the Guiness Book of World Records. The book was first published in 1955, I was born in 1960, and 2^11213-1 seems to have been the record prime between 1963 and 1971. With 3,376 digits, it would have easily fit on a page. To put this in perspective, I just downloaded a file containing the digits of 7,235,733 digits of 2^24036583, the recently-discovered current largest known prime. The enormity of these numbers sometimes does not register. Out of curiosity, I checked to see what is the smallest number which is not a substring of this new prime's digits, and it was 101679. - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"

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[math-fun] Triangle question
by David Wilson 07 Mar '05

07 Mar '05

What triangles with (a, b, c) = 1 have curcumradius/inradius = integer? - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"

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[math-fun] Flat Maze sequence
by Eric Angelini 04 Mar '05

04 Mar '05

Hello math-fun and SeqFan, I don't know if this is old hat -- if yes please ignore. Rules for a new arrangement of the natural integers : 0) At the beginning there was a (semi)-infinite row of empty labels; 1) Then came the Pencil who wrote "1" on the first (most- left) one; 2) "1" meant: "write now whatever integer you want (but not used so far) on the label to the right of me at a distance of "1" step; [and, more generally, an odd integers means: "go 2k+1 labels to the right and write smthg new on it -- the label must be blank, though". An even integers means: "go 2k labels to the left and write...".] Question: is there an algorithm to rearrange all the na- tural integers with those two simple rules (leaving no empty labels behind) ? I have started this possible sequence (a dot means "still empty label"; the next label to be named has an "x"): 1 3 5 7 2 11 15 4 17 13 9 6 21 23 25 27 10 . . 8 . 12 14 . 17 19 . . . . . . . 20 . . 22 . . 24 . x 18 . 32 . . . . . This sequence looks like an "flat maze" -- thus the name. The above has been done by hand -- this explains why the rows are 10 integers long: labels are easier to reach be- cause a vertical step (downwards) adds 10 to the count. Best, É.

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[math-fun] Re: Tool for writing mathematical documents
by David Wilson 04 Mar '05

04 Mar '05

Thanks for all the suggestions on a math paper tool. I guess I should have been more specific. --------------------------------------------------------------------------------------- Choice of language I am stuck with Windows XP Home, and I am sometimes tempted to write papers for the JIS, but I'm daunted by the task. If I had looked at the current JIS home page, I wouldn't have had to ask about the format, since the JIS accepts only LaTex documents. That settles the format issue. Besides, the overwhelming majority of recommendations were to use LaTeX anyway. AMS articles require AMS LaTeX, but I don't think I'm in danger of writing one of those for the moment. I am not exactly sure what TeX is all about. I used to think it was pretty much a markup language, a format as it were. But now it appears that there are associated fonts and other baggage. I'll have to educate myself better on TeX. I'll check out MikTeX when I can. --------------------------------------------------------------------------------------- Choice of editor With regards to wysiwyg equation editor versus text editor, I think it is a moot issue. The best of all possible worlds includes both. The equation editor makes the big projects and messy equations tractable and gives you a view of the final product, while the text editor helps you do the fine tuning. Most enviroments have at least a text editor, so the issue boils down to whether the word processor includes an TeX-capable equation editor. Here are the suggestions I got for editors: TeXmacs. On the plus side, a true TeX editor. Installs under Cygwin, which I already use. Looks as if the TeXmacs project envisions broad support for TeX. On the downside, I'm not a Lisp weenie, so emacs will be a learning curve. Hopefully one can configure and use emacs without having to know Lisp indepth. Also, I remember that emacs used to have a "vi" mode for us "vi" weenies. Definitely worth a look. OpenOffice. I had a short experience with StarOffice, a precursor to OpenOffice, as a means to deal with MS Word files on an UNIX system. I don't know much about the Writer word processor. It seems to have equation writing capabilties, but is not TeX capable. Open to education on this point though. TeX Live and Kile appear to be non-Windows; ego I can't use them. MS Word. I am a reluctant Microsoft user. I hear the warnings that MS Word has problems for large documents, and I believe it. MS apps aren't widely used because they are reliable. I'm still using Word '97. I haven't tried Works Word Processor. Word has a pretty lame equation editor, which can be upgraded to Design Science's MathType editor for $130. MathType apparently gives you math capabilities in Word, HTML, and the major TeX variants. I have had good experiences with Design Science's MathPlayer. As far as Eequation suggested by Steve Gray, I can't seem to find it on the Web, a link would be good. If I choose to avoid MathType, I can use Chikrii Softlab's Word2Tex to convert Word to TeX, for $99. Also, I heed the warnings that MS Word itself has problems for large documents. ASCIIMathML will be very useful to me, thanks Mr. Stay. - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Shickele, from P.D.Q. Bach's oratorio "The Seasonings"

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[math-fun] ArXiv.org
by David Wilson 03 Mar '05

03 Mar '05

Someone suggested to me ArXiv.org as a source of TeX documents. I go there and, wow, right away I find: A proof the ZF is inconsistent (math.GM/0502503), and a formula for twin primes (math.GM/0502384), and a 7-page proof of FLT (math.GM/0309005). Why is this site not better publicized? I feel like the good stuff is being held back...

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