May 2016 - mathfun@mailman.xmission.com

[math-fun] binomial^n = binomial
by Bill Gosper 13 May '16

13 May '16

Are there any more of these? (2^(2/3) - 1)^4 = 12*2^(1/3) - 15, (10^(1/3) - 1)^5 = 99 - 45*10^(1/3), (5^(1/3) - 2^(1/3))^6 = 63*2^(2/3)*5^(1/3) - 171 . --rwg

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[math-fun] Website with nice math problems
by Robert Baillie 13 May '16

13 May '16

I don't know how I stumbled across this, but I find most of the entries in this blog to be quite interesting: http://datagenetics.com/blog.html Bob

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[math-fun] USC's in-memoriam for Golomb
by Hilarie Orman 13 May '16

13 May '16

"Golomb, who began his career at the USC Viterbi School of Engineering in 1963 and continued to teach a freshman seminar well into his 80s, was known for his singular ability to apply advanced mathematics to problems in digital communications. Video images from the Mars Rover Curiosity owe a huge debt to Golomb’s mathematical coding schemes, enabling pristine imagery transmitted from the Mars Rovers all the way back to Earth. His work on shift-register sequences is integral to the function of cellular phones, while his cryptology research ushered in new approaches for securing communications signals." Full story: http://news.usc.edu/100264/in-memoriam-solomon-golomb-communications-techno…

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[math-fun] Square into integer sided triangles
by Ed Pegg Jr 13 May '16

13 May '16

Was Richard Guy misquoted? http://blogs.scientificamerican.com/guest-blog/martin-gardner-at-101-it-s-a… states: Another puzzle from 1989 that remains unsolved to this day, credited to Richard Guy, asked if it is possible to triangulate a square with whole number side lengths such that the resulting triangles also have whole number side lengths? --------------------------------------------- Here's an interesting, not-too-hard puzzle inspired by that. Divide a 12x12 square into the fewest number of integer-sided triangles. If you solve it, gloat about it, but don't give the answer. --Ed Pegg Jr

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[math-fun] Draft of my May 2016 blog post
by James Propp 12 May '16

12 May '16

Hi, I started writing a new draft titled "Fermat's Last Theorem: The Curious Incident of the Boasting Frenchman" and would love to get your feedback. I plan on publishing it on the morning of May 17th. <https://mathenchant.wordpress.com?p=731&shareadraft=57355e11379d2> Read it at: https://mathenchant.wordpress.com?p=731&shareadraft=57355e11379d2 Please leave your feedback here: https://mathenchant.wordpress.com?p=731&shareadraft=57355e11379d2 Keep in mind that all feedback is by default anonymous; I won't be able to reply to your comments (if, say, you have questions) unless you say who you are. Thanks, Jim Propp

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[math-fun] 473-gene "artificial bactierium"
by Warren D Smith 12 May '16

12 May '16

Venter et al made their long-awaited "artificial bacterium" (actually synthetic DNA that they managed to get inside a bacterium to "boot up" a wholy artificial design for living being, which of course was based on 473 known natural genes). They think or hope that 473 is near minimum possible. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] ancient earth allegedly had thin atmosphere
by Warren D Smith 11 May '16

11 May '16

Sanjoy M. Som, Roger Buick, James W. Hagadorn, Tim S. Blake, John M. Perreault, Jelte P. Harnmeijer & David C. Catling: Earth's air pressure 2.7 billion years ago constrained to less than half of modern levels, Nature Geoscience March 2016 http://www.nature.com/ngeo/journal/vaop/ncurrent/full/ngeo2713.html claims air bubbles in lava show the Earth's atmosphere at sea level 2.7 Gyr ago, was roughly comparable in pressure to today's top of Mt.Everest. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] 2.7 bya atmosphere ~0.5 bar
by Henry Baker 10 May '16

10 May '16

FYI -- I'm still curious about the atmosphere in the 0.065 - 1 bya time period. This paper indicates that nitrogen was actively being removed from the early (2.7 bya) Earth atmosphere by *organisms* -- something that apparently never happened on Venus. https://www.washingtonpost.com/news/speaking-of-science/wp/2016/05/10/secre… Secrets of life on early Earth Â and other planets Â may be trapped in ancient gas bubbles The culprit was probably tiny organisms that sucked nitrogen Â the element that makes up about 80 percent of the atmosphere Â from the air. That process, called nitrogen fixing, still happens today, but the gas that is removed is replaced by other biological processes. The organisms that release nitrogen back into the air rely on oxygen, a gas that wouldn't become available in the atmosphere until the Great Oxidation Event a few hundred million years later. http://www.nature.com/ngeo/journal/vaop/ncurrent/full/ngeo2713.html Earth's air pressure 2.7 billion years ago constrained to less than half of modern levels How the Earth stayed warm several billion years ago when the Sun was considerably fainter is the long-standing problem of the 'faint young Sun paradox'. Because of negligible1 O2 and only moderate CO2 levels in the Archaean atmosphere, methane has been invoked as an auxiliary greenhouse gas. Alternatively, pressure broadening in a thicker atmosphere with a N2 partial pressure around 1.6Â2.4 bar could have enhanced the greenhouse effect. But fossilized raindrop imprints indicate that air pressure 2.7 billion years ago (Gyr) was below twice modern levels and probably below 1.1 bar, precluding such pressure enhancement. This result is supported by nitrogen and argon isotope studies of fluid inclusions in 3.0Â3.5 Gyr rocks. Here, we calculate absolute Archaean barometric pressure using the size distribution of gas bubbles in basaltic lava flows that solidified at sea level ~2.7 Gyr in the Pilbara Craton, Australia. Our data indicate a surprisingly low surface atmospheric pressure of Patm = 0.23 Â± 0.23 (2 ) bar, and combined with previous studies suggests ~0.5 bar as an upper limit to late Archaean Patm. The result implies that the thin atmosphere was rich in auxiliary greenhouse gases and that Patm fluctuated over geologic time to a previously unrecognized extent.

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[math-fun] matchstick graphs
by Warren D Smith 10 May '16

10 May '16

Allan Wechsler is of course correct, K-regular matchstick graphs exist with 2^K vertices and graphically the same as the K-cube. (if edge-crossings allowed.) These evade my degree of freedom counting argument because his graph drawings "really" have very few, about 2K or fewer, degrees of freedom.

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[math-fun] Something special about 104
by Paul Palmer 10 May '16

10 May '16

(Delurking for my first post.) A while back I saw a fact posted (on Pat's Blog, if anyone reads it) that said: 104 is the lowest known number of unit line segments that can exist in the plane, 4 touching at every vertex. I can find this repeated all over the internet, but nothing more about it. I read it as saying that the smallest 4-valent (quartic) unit distance graph has 104 vertices. Does that sound correct? Does anyone know where this might have come from? Thanks. I have enjoyed following the discussions on this list.

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