The second delivery, (the previous post continues 1552.-2nd Mathematical Carnival 1/2) with other categories that arbitrarily I called theory, problems and art:
It has been a real pleasure to read the posts: to learn new things, to remember forgotten others, to verify that several are interested in certain topics.
For the time being, except error or omission of my part, I declare the 2nd Edition closed, and spend the task to Rafael for the next one.
Theory
The cicloide: what is the shortest way?: Gaussianos speaks to us about the cicloide with his everlasting clarity. Nevertheless, instead of demonstrating mathematically the properties that the curve has, it demonstrates them to the physical thing, with two experimental videos! Good variant of a blog that does publication seriously, and usually does not hide the accounts!
Why are any antennas parabolic?: Matgala brings the geometric definition of the parable, and how this implies that the beams perpendicular to the guideline are reflected happening for the focus. There is behind this a pseudohistory of the very widely used science (Arquímedes setting fire to ships), which turned out to be compiled then for the Persons of encyclopedic learning of the Roman Empire. Some years later, the Arabs worried for the possible existence of such weapon of long scope. Ibn Sahl (940-1000) would write then a work "The Incendiary Mirrors" where it would introduce the study of the lenses, and would discover the Snell law. There is a partial translation to our language, in S. Cerantola, Shelf of Arab studies, 2004 (I leave the link in the Matgala blog to the pdf).
Atractores and hurricanes, and Fractales: E. Gracián speaks to us about atractores, chaotic systems and fractales, and The manifesto of the group brings us over "Art and Complexity" of "Movement Fractalista" that per moments class seems bulging of a movie B, and in others of that article of Sokal. On the confusion chaos - azar-complejidad, I recommend to them the end of his first post, and a deeper discussion on the 'reality' of a 'reality fractal', in:
II carnival of Mathematics: The nature prefractal of the Nature: Francis brings over to us a discussion of 12 years ago, route articles and letters in Nature, where there questions this habit of seeing fractales in all sides. The example of the coasts is one of questioned so many people. A few years later, with the topic of the distribution of the grades of the nodes in the free scale networks also supposed potency laws), the same type of discussion was re-lived in Science and Nature.
The size of the sets: Zurditorium continues with the topic of 1er Carnival, and gets with many clarity into the demonstration of which the cardinal one of parts of a set is major than the cardinal one of the original set. This observation clear in finite sets, generated different debates on the possibility that there existed or not a set bigger than all the sets.
Body goes!: Tito Eliatrón shows us a body, and later not what he keeps on saying. In fact yes: it gives the body axioms, and gets with some of the habitual bodies into mathematics. Nevertheless, as it indicates him M in the comments, the smallest body is that of the only element, F1, that in fact does not exist because the axiom 5 speaks about the existence of neutral two. But as Stanislaw Lem says, "the banality of the existence has been proved too many years ago so that he was worth while dedicating one more word", and the mathematicians him have paid attention, they devoting to work on something that does not exist!
Of cars registrations and tenth of lottery: Rafalillo faces a complicated topic. The results equiprobables are, skylight, equiprobables, although sometimes some of them seem less probable than others to us. Nevertheless, at the time of taking decisions - on playing the lottery or not, between others - it is never of more bearing in mind the Tartaglia phrase: "The imperfection of the matter causes effects in the machines that do not coincide with the abstract geometric demonstrations".
Friendship between Numbers: "things" the work takes of summing up and there translates the article Friends in High Places of Roger Webster and Gareth Williams who appeared in Mathematical Spectrum (it is possible to find the link at the end of his post).
Potentials calculation: Noxbru publishes a method númerico to calculate the value of the electrical potential. It brings near doing Taylor (the Nirvana for these things, like comment in another post of the carnival), and the convergence justifies itself easily for the property of the average value of the laplaciano. I do not excuse to myself that this post was passing to me on a topic that I like so much...
Vectoriales fields as explanation to the maelstrom of our hair: Lagu writes on the theorem of the shaggy dog, and - very original - it does not mention this name. There is some confusion in the post, or it is me who is that I do not manage to understand it, because half a head yes can comb without hair getting up (and it mentions it in a paragraph but he denies it in the following one), and neither the theorem of the difference is the explanation of this result.
Problems
Carnival of Mathematics II: Sequential pastime and [CMII] Connect: the corner of the series: Zifra leaves a sequence to us to resolve, and linkea the list of Snark, the place of Marcia Levitus, and the Encyclopedia of Successions of Entire Numbers of Sloane. Snark - leaving aside Lewis Carroll - was the name of a mythical Argentine magazine of games of ingenuity, ten numbers published between '76 and '78, replaced in '78 for Humor and Games (it had little more than hundred editions, but the publishing People of Mind still keep on editing books and magazines). Later, from '83 edited Brains in Spain (with a similar subject-matter, and collaborators together). It turns out to be difficult to measure the influence that this magazine had in me to me, and on the day of today it keeps on being a pleasure to cover blogs where this spirit is still alive. Ah, and the solution is...
Carnival cryptosum: 26 is one of the most original acertijeros that I meet. Did I already say it earlier? Yes, but since today there will be many new people somewhere here, I am useful to repeat it. Apart, the definition 5 is a sample of his big humor; as the priest was saying in the stories of Canterbury "to whom him that might have occurred!"
Another problem of probabilities: Gustavo (with Ivan, Markelo and 26, one the persons that more I associate like heirs of H&J) leaves to us different variants of a classic problem, and I am grateful to him that he will send it to me for mail on Monday, since I had time to include it in the final examination of Honest of tomorrow ;)
Thousand wine bottles: Zurditorium adds a problem that we can consider an outstanding figure.
Art
Musical geometry: The waves Eva M brings to us another entry, which in my case turns out to be very nearby to me. I have to struggle not to speak about autovalues, the badges of Chladni, the nodose lines... In his blog linkeo an old man post mine on the topic.
Espiraleando: Carlo mixes music with Fibonacci, in a really original post. This is the comment that later in writing, because it was not finding the author of a delightful text, which had known thanks to the Pseudópodo blog. Finally, I had to consult with him what the post would be, and in minutes it found the reference: Spirit and Nature, of Gregory Bateson. There is a phrase in this text that it wears just here:: oh, it has a spiral! It must have belonged to something living. But it is not the only coincidence: Bateson taught artists in California (there the group Tool arises, decades despuñes); other one of the songs of this band is "Schism"... term that Bateson introduced in anthropology, and that the proper band Tool understands like "to separation or division into factions". I could not find concrete tracks of a link between Bateson and Tool, but the common ideas and the influences I believe that they are very clear.
Mathematics carnival: Ann leaves a poetry to us, Deriving adrift. Let's be useful to remember that it took fifteen days to the proper Leibniz to discover the rule of derivation of the product...
Germán Díaz: the Pi music: Pachi Carpet does an interview to the musician Germán Díaz, who dedicated a song a disc to this number. It has also a "mathematical lullaby", and both can be listened in youtube. A separate comment would be deserved by the devices that Germán uses, especially the organ to perforated cards that goes back a XIXth century, it designs that the looms of the epoch were used also, and that it inspired in Babbage another type of machines...
Geometry of the flakes of snow: Milhaud brings to us a post on the flakes of snow, which I go to allow to include in this category. I add in his post two links that he should share, the original Kepler work, and a place to design snow flakes.
Lime and Sand: José Maria brings to us two images of Saragossa, one of lime and other one of sand. The second one... perhaps is a maneuver to receive more expensive the same. A real matematicidio, as José Maria says.
Histories of Pi the pirate: Eva M brings the 2nd episode of the history. [It seems logical to me that and be the abordo second one, only root of two might dispute this honor, but it is not such a transcendent number].
I in broken do not get: Tito brings to us a fragment of a movie of Woody Allen... that I forgot to include!
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