June 2018 - mathfun@mailman.xmission.com

[math-fun] Your new inverter
by Bill Gosper 06 Jun '18

06 Jun '18

On 2018-06-06 02:05, Simon Plouffe wrote: > you may try this too : > > http://plouffe.fr/pi/main/public/ > > it is the inverter, new version in beta test. > > 11.3 billion entries. > > Simon Plouffe > > > Le 2018-06-06 à 09:13, Bill Gosper a écrit : >> 1/2 + 1/(2 + π) Nice! Glitches: Prompt says 6 digits! Means ≥6. 0.6944922648241714 is properly rounded from 0.694492264824171355, but gave no hits. 0.694492264824171 worked. --rwg

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[math-fun] alicenapism? It's a cognate!
by Bill Gosper 06 Jun '18

06 Jun '18

Google Translate from Turkish: Türk'lerin İslam'ı seçmeden önceki töresi ile Müslümanlık arasında birbirine benzeyen bir çok husus bulunmaktaydı. Bu hususları; tevhid inancı, temizlik, hoşgörü, dürüstlük, alicenaplık, adalet, eşitlik, ahirete iman, kurban, cihat, ganimet, aileye ... To "English": There were many similarities between Muslims and the customs of the Turks before the election of Islam. These include; tevhid belief, cleanliness, tolerance, honesty, alicenapism, justice, equality, belief in the afterlife, sacrifice, jihad, booty, family ... Tayyip Erdogan sometimes uses alicenaplık to mean covfefe. --rwg SPOILER: http://tureng.com/en/turkish-english/alicenapl%C4%B1k

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Re: [math-fun] alicenapism? It's a cognate!
by Dan Asimov 06 Jun '18

06 Jun '18

Have not checked spoiler link, but just tried same quoted passage and got: ----- Between the ceremony before the election of the Turks and Islam there were many similarities. These include; monotheism belief, cleanliness, tolerance, honesty, tolerance, justice, equality, afterlife faith, sacrifice, jihad, booty, family ----- So I think the meaning of alicenapism has been made quite clear. In fact I myself am a longtime alicenapist. —Dan Bill Gosper wrote: ----- > Google Translate from Turkish: >Türk'lerin İslam'ı seçmeden önceki töresi ile Müslümanlık arasında >birbirine benzeyen bir çok husus bulunmaktaydı. Bu hususları; tevhid >inancı, temizlik, hoşgörü, dürüstlük, alicenaplık, adalet, eşitlik, ahirete >iman, kurban, cihat, ganimet, aileye ... > >To "English": >There were many similarities between Muslims and the customs of the Turks >before the election of Islam. These include; tevhid belief, cleanliness, >tolerance, honesty, alicenapism, justice, equality, belief in the >afterlife, sacrifice, jihad, booty, family ... > >Tayyip Erdogan sometimes uses alicenaplık to mean covfefe. --rwg > >SPOILER: >http://tureng.com/en/turkish-english/alicenapl%C4%B1k -----

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Re: [math-fun] Packing parallelograms into a triangle
by Dan Asimov 06 Jun '18

06 Jun '18

(spoiler below for the first question) Jim Propp wrote: ----- Puzzle: Show that a triangle cannot be written as the union of a finite number of parallelograms with disjoint interiors. Puzzle: Show that you can cover n/(n+1) of the area of a triangle using n parallelograms with disjoint interiors. Problem: is it possible to do better? ----- Nice question! (SPOILER ALERT) ----- Starting from one side of the triangle, each parallelogram must share a side with a new adjacent parallelogram having a new parallel side. This cannot be one of the triangle sides, since those cannot be parallel, contradicting the finiteness of the set of parallelograms. ----- (Incidentally, with countably infinitely many parallelograms, it's possible to cover the interior and two sides of a triangle, but I'm not sure if the entire third side can be covered; I suspect not.) —Dan

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[math-fun] ISC: 0; ries: 1
by Bill Gosper 06 Jun '18

06 Jun '18

Given 1/2 + 1/(2 + π), https://isc.carma.newcastle.edu.au/advancedCalc "really found nothing." ries took 4msec: Your target value: T = 0.694492264824171 mrob.com/ries . . . x-1/2 = 1/(2+pi) for x = T - 1.11022e-16 {78} --LHS-- --RHS-- -Total- max complexity: 44 38 82 dead-ends: 9401 11053 20454 Time: 0.004 expressions: 516 441 957 distinct: 444 347 791 Memory: 61136 B Total equations tested: 154068 (1.541e+05) But ISC knows scads more exotic constants and functions. --rwg Now my only problem is that .6944... is the difference between two quantities I thought were equal.

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[math-fun] Packing parallelograms into a triangle
by James Propp 05 Jun '18

05 Jun '18

Puzzle: Show that a triangle cannot be written as the union of a finite number of parallelograms with disjoint interiors. Puzzle: Show that you can cover n/(n+1) of the area of a triangle using n parallelograms with disjoint interiors. Problem: is it possible to do better? Jim Propp

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[math-fun] Sec@n/n →0??
by Bill Gosper 05 Jun '18

05 Jun '18

Abs exceeds 9 for four of the first thousand convergents of π/2: [62]:= Select[Sec[#]/# & /@ Numerator@Convergents[π/2, 999], Abs[#] > 9 &] //tim During evaluation of In[62]:= 0.213593,4 Out[62]= {Sec[11]/11, Sec[214112296674652]/214112296674652, Sec[1428599129020608582548671]/1428599129020608582548671, Sec[63008132762960627316194351129]/63008132762960627316194351129} And no others among the next hundred thousand! In[63]:= Select[Sec[#]/# & /@ Numerator@Convergents[π/2, 99999], Abs[#] > 9 &] //tim During evaluation of In[63]:= 25.228223,4 Out[63]= {Sec[11]/11, Sec[214112296674652]/214112296674652, Sec[1428599129020608582548671]/1428599129020608582548671, Sec[63008132762960627316194351129]/63008132762960627316194351129} !?! In[64]:= N[N[%, 33], 9] Out[64]= {20.5411872, 18.0078002, 11.5073819, 16.8247791} And none negative. Wouldn't Gauss's Log[2,1+tail] probability predict a fairly steady, non-tapering stream of qualifiers? --rwg On Sat, Jun 2, 2018 at 12:00 AM, Bill Gosper <billgosper(a)gmail.com> wrote: > Out[42]= Sec[18190586279576483]/18190586279576483 > > In[43]:= {N@%, N[%, 22]} > > Out[43]= {-6.53302256185329*10^-17, 2.154106494388454341277} > --rwg > Does |Sec@n/n| (integer n) have a supremum, or even a simple max? > Hopelessly difficult: The minimal p for which Sec@n/n^p has a limit. >

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[math-fun] Testing 2, 3, 9, ...
by Henry Baker 04 Jun '18

04 Jun '18

This is just a test. If this had been an actual email, you would have been instructed to switch to ASCII from EBCDIC.

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Re: [math-fun] Leyland primes
by Keith F. Lynch 04 Jun '18

04 Jun '18

Hans Havermann recently mentioned Leyland primes (primes in the form x^y + y^x), so I looked them up on OEIS. I expected to see a bunch of random-looking odd numbers. And for the most part, that's what I saw. But I noticed that some of them have remarkably long runs of 0s. For instance the 30th term is a 465-digit decimal number, of which 305 consecutive digits are 0. And the 37th term is a 613-digit number of which 417 consecutive digits are 0. Why should that be? And does something similar happen in other radices? Thanks. One possibility is that in those cases y^x is much greater than x^y and y is divisible by 10. If so, I'd expect that I'd find primes in the form x^y - y^x to often have long runs of 9s. I found a list at A123206, and see that that is indeed the case. So I guess that's the explanation.

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[math-fun] Parametrization of the sphube
by françois mendzina essomba2 03 Jun '18

03 Jun '18

The points of the sphube of radius of axis r and center the origin of the mark can be parameterized by: x=r*(qos(theta))*(qos(phi)); y=r*(qos(theta))*(qin(phi)); z=r*qin(theta); theta in [sigma/2,-sigma/2]; Phi in [sigma,-sigma]; for the sphube x ^ 4 + y ^ 4 + z ^ 4 = 1 we have: r = 1

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