June 2016 - mathfun@mailman.xmission.com

[math-fun] Speaking of arithmetic puzzles
by Leo Broukhis 17 Jun '16

17 Jun '16

X/1 + X/2 + X/3 + X/4 - X/12 = 1 1 / (X/2 + X/3) = X/7 The meaning (not "value") of X is the same in both equations. What is the meaning of X? Or, more specifically, which Unicode character does X stand for? Leo

1 0

[math-fun] puzzle on Facebook
by Bill Gosper 17 Jun '16

17 Jun '16

On 2016-06-17 08:57, Joerg Arndt wrote: > * Dan Asimov <dasimov(a)earthlink.net> [Jun 17. 2016 08:06]: >> In the world of newspapers, nothing the Daily Mail claims can be trusted. >> > > I think you spelled "Daily Fail" incorrectly 8^) > >> They have zero journalistic ethics. >> >> So am not at all surprised that they're spouting nonsense here. >> >> I seem to recall that a few years ago they printed a story about >> someone who discovered that, contrary to what all mathematicians >> had erroneously believed, you actually *can* divide by zero in >> ordinary arithmetic. > > That one went into several newspapers with non-zero reputation > as well. Now consider that (at least here in Krautistan) one > can study "technical journalism", look at the science/technology > articles in the well-established newspapers, and silently weep. > > Btw. the German version (mostly translation, but some added material) > of the "Scientific American" banned formulas altogether (I heard there's > one exception: you may say E = m c^2, once, and get away with it). > [Is the same true for the original?] They *must* have allowed Gardner's column a few formulas. But it got completely ridiculous with their Ramanujan article. Their solution was to print *photographs* of his equations with "explanatory" captions! I ran afoul of this when the editors of More Mathematical People read Hawking's remark that each printed formula reduces your book sales by 50%, so they yanked all my formulas (and fractal diagrams). All I could do was tell them where to go when they wanted my permission for a Japanese edition. --rwg > They once had a piece about what's in the (lovely) article > Michael Kleber: Goldbug Variations, > http://arxiv.org/abs/math/0501497 > ... their "popularized" version was completely incomprehensible. > > Best regards, jj > > >> >> —Dan >> >> >> > On Jun 16, 2016, at 4:57 PM, Henry Baker <hbaker1(a)pipeline.com> wrote: >> > >> > FYI -- Better fire that math teacher and Professor Puzzler; maxima trivially solves this puzzle (follow link to jpeg of the equation set) and it has a unique answer. >> > >> > "Brain-splitting equation that even a MATHS TEACHER can't solve has the entire Internet baffled... So do YOU know the answer?" >> > >> > http://i.dailymail.co.uk/i/pix/2016/06/16/07/3555F68A00000578-0-image-a-6_1… >> > >> > "A simple logic and maths puzzle has sparked debate on Facebook after thousands of people have debated over the answer. The puzzle, which replaces numbers with flowers, has caught thousands of people out. A maths teacher who solves logic puzzles online and goes by the name of 'Professor Puzzler' even refused to solve it, saying the problem had no answer." >>

1 0

[math-fun] puzzle on Facebook
by Henry Baker 17 Jun '16

17 Jun '16

FYI -- Better fire that math teacher and Professor Puzzler; maxima trivially solves this puzzle (follow link to jpeg of the equation set) and it has a unique answer. "Brain-splitting equation that even a MATHS TEACHER can't solve has the entire Internet baffled... So do YOU know the answer?" http://i.dailymail.co.uk/i/pix/2016/06/16/07/3555F68A00000578-0-image-a-6_1… "A simple logic and maths puzzle has sparked debate on Facebook after thousands of people have debated over the answer. The puzzle, which replaces numbers with flowers, has caught thousands of people out. A maths teacher who solves logic puzzles online and goes by the name of 'Professor Puzzler' even refused to solve it, saying the problem had no answer."

9 9

Re: [math-fun] puzzle on Facebook
by Henry Baker 17 Jun '16

17 Jun '16

Here's another solution, noticing that there are *two* yellow flowers in the third equation: Maxima 5.28.0-2 http://maxima.sourceforge.net using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) r+r+r=60; (%o1) 3 r = 60 (%i2) r+b+b=30; (%o2) r + 2 b = 30 (%i3) b-2*y=3; (%o3) b - 2 y = 3 (%i4) solve([%o1,%o2,%o3],[r,b,y]); (%o4) [[r = 20, b = 5, y = 1]] (%i5) y+r*b,r=20,b=5,y=1; (%o5) 101 (%i6)

1 0

Re: [math-fun] puzzle on Facebook
by Henry Baker 16 Jun '16

16 Jun '16

My eyesight isn't so good, so I simply focused on the colors of the flowers. So, modulo everything but colors, we have: Maxima 5.28.0-2 http://maxima.sourceforge.net using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) r+r+r=60; (%o1) 3 r = 60 (%i2) r+b+b=30; (%o2) r + 2 b = 30 (%i3) b-y=3; (%o3) b - y = 3 (%i4) solve([%o1,%o2,%o3],[r,b,y]); (%o4) [[r = 20, b = 5, y = 2]] (%i5) y+r*b; (%o5) y + b r (%i6) %,r=20,b=5,y=2; (%o6) 102 (%i7)

2 1

[math-fun] ear-mathematicians and eye-mathematicians
by James Propp 15 Jun '16

15 Jun '16

Can anyone provide a source or quote for the dichotomy between "ear-mathematicians" (algebraists) and "eye-mathematicians" (geometers)? I tried Google, but had no luck. Thanks, Jim Propp

5 4

[math-fun] Am I reinventing the wheel?
by Leo Broukhis 15 Jun '16

15 Jun '16

Dear Math-Funsters, As an aspect of my Soviet retrocomputing recreations, I'm trying to extract the font of the original drum printer used before the beginningt of the infamous IBM-cloning program by the Eastern bloc. The starting point is a fairly low-quality (200dpi) scan of a very low quality printout of the diagonal test: http://besm6.sourceforge.net/static_gallery_mirror/images/21_1.jpg (the printer was ~40 years old and the ribbon likely hasn't been re-inked for many years). The charset is GOST-10859. I was able to segment the image into individual tiles 21x33 px automatically using maxima of average intensities per line and per column, accounting for some downward drift toward the right side and the fact that the glyphs are top-heavy due to dot gain as a result of drum surface velocity orthogonal to hammers' velocity . (~100 C++ lines) Then I've implemented a homebrew super-resolution algorithm by iteratively finding min. mean square error per pixel of the overlapping rectangle (i.e. dividing the sum of squared errors by the number of pixels squared to disfavor matching empty corners with empty corners) of the average collected so far and every tile per codepoint. The non-adaptive mean of all tiles, with some contrast enhancement, is used as the seed for the algorithm. (also ~100 C++ lines). (For better results, tiles are normalized (pnmnorm) and edge-enhanced (pgmenhance or pnmnlfilt) before running the super-resolution, and the result is normalized again. This yielded http://mailcom.com/besm6/acpu/enhanced/ As you can see, the top-heavy dot gain is still quite pronounced (e.g. compare the serifs of I, code 102). Then I tried to experiment with erosion algorithms. Straight erosion (new value of a pixel = max({R-nbrhd(pixel)}) is too strong, eating away weak lines. I've came up with new.val = max(cur. pixel, max({R-nbrhd})+min({R-nbrhd})-mean({R-nbrhd \ cur. pixel})) NB that excluding the current pixel from the mean is important to leave a pixel surrounded by white pixels unchanged. This is a much more gentle erosion than the straight maximum. As an experiment, I've changed the formula to be new.val = max({R-nbrhd})+min({R-nbrhd})-mean({R-nbrhd \ cur. pixel}) to see what happens when it is erosion-dilation indifferent. The result is very amusing: http://ic.pics.livejournal.com/spamsink/7162160/44779/44779_original.gif (iteratively applied to the output of 'pgmramp -e 100 100', R = 2.5, neighborhood size 21 pixels) Is there anything I could have done better? Are there smarter super-resolution algorithms? Erosion algorithms? Am I reinventing the wheel with the "water circles" formula new = max({R-nbrhd})+min({R-nbrhd})-mean({R-nbrhd \ cur}) ? Thanks, Leo

4 4

Re: [math-fun] ear-mathematicians and eye-mathematicians
by Bill Gosper 15 Jun '16

15 Jun '16

On 2016-06-15 12:35, Fred Lunnon wrote: > Mmm ... What about analysts --- "ass-mathematicians"? > > [No, really --- some of my best friends are analysts. Well, were, anyway ... ] > > WFL Fred, you are willfully smudging the distinction between pure and applied proctology. --rwg > > > > On 6/15/16, James Propp <jamespropp(a)gmail.com> wrote: >> Can anyone provide a source or quote for the dichotomy between >> "ear-mathematicians" (algebraists) and "eye-mathematicians" (geometers)? >> >> I tried Google, but had no luck. >> >> Thanks, >> >> Jim Propp

1 0

[math-fun] Dissection problem
by David Wilson 12 Jun '16

12 Jun '16

1. Dissect a triangle of your choice into n > 1 triangles with all 3n edge lengths distinct. 2. Same question for a quadrilateral of your choice.

8 15

[math-fun] Very cool new stone vault structure using 100% compression
by Bill Gosper 11 Jun '16

11 Jun '16

On 2016-06-11 12:03, Henry Baker wrote: > May I pass "Martin's Marbles" pix on to Philippe at block(a)arch.ethz.ch ? > Surely! > Do you have a reference to the eponymous "Martin" ? A bit of ribbing of Martin Gardner, who predicted gosper.org/3dsno.png would be "smooth as a marble" --rwg > > At 07:30 PM 6/9/2016, Bill Gosper wrote: >>I'm surprised they didn't use Martin's Marbles technology >>gosper.org/dodex.gif >>gosper.org/martinsmarbles.png >>which is indifferent to the sign of g. --rwg >>On 2016-06-08 16:02, Henry Baker wrote: >>> (Watch the 4.5 minute vimeo video using the link below to see the >>> structure being built.) >>> >>> Look ma, no mortar! >>> >>> Dr. Philippe Block (no kidding!!) is from MIT. >>> >>> http://www.wired.com/2016/06/compression-keeps-24-tons-stone-collapsing/ >>> >>> https://player.vimeo.com/video/167868985 > >

1 0