1539. - Roots

I pseudoprune, descendés of the monkey, like all :-)

it is an entertaining pastime, if a group of physicists puts himself, they have the most difficult part made, because the 'old' physicists are already almost all: Bohr, Heisenberg, Einstein, Sommerfeld... (and the oldest, with more reason: I found round there Ohm, now I have to add the Huygens line in Leibniz, etc)

1540. - Jueguitos

I recommend to them to prove the chat to nongo. In this game there is an element random, that joined a limited board, alters the theory known for the game of the Angel.

On this another game, we can say that it is almost liquidated: four demonstrations say that the angel wins if it is allowed to the angel to give two steps. But if the angel moves of one, as a king in a Chess board, is cooked. Very good summary of the demonstrations and links to the papers, here.

And, to relax the mind, an abstract jigsaw puzzle, sencillito, without images that they distract.

1542. - Omerta

(we go, carajo!! I am returning: newly it was going to put bold faces, and instead of the code html usually, I appealed to the téxico textbf {})

* * *

(mmm... and now I started begin {center}, before realizing..., fault of that is not a question of not postear either!!)

* * *

Exercise: analyze the Quandary of the Prisoner in case (at least) one of them belongs to the mafia (*).

* * *

If the DdelP does not know, two citizens are detained and isolated up to confessing a crime and accusing other. If they do not do it, prisoners go 3 years c/u. If the two do it, prisoners go 10 years c/u. If one does it and other not, that speech goes out freely and other goes 15 years prisoner.

* * *

Omerta comes, it was creating or not, of hombredad, prudently replaced in our language for manliness.

* * *

(*) if it is necessary to clarify it, the Omerta is the categorical prohibition (**) of cooperating with the police authorities, still having been a victim of a crime.

* * *

(**) With arrows and everything!

* * *

Advanced exercise: in a population of N you present yourself, pN they are of the mafia (p between 0 and 1). The police choose a pair at random and they play the DdelP. How does the percentage of gangsters endure after k games? (suppose that they are realized before nobody remains free)

(if someone wants to catch fire, we write something)

1543.-Three theorems on the water and his absence of form

Teor 1: Imagenemos a river, and let's put a hexagonal network in a part of the watercourse, between two coasts. We choose hexagons at random, and place in them a cement column (if two are nearby, they join hermetically).

Only there are two possible results: or a water course remained open, or the columns form a dike. Finally, all Hex game ends with the victory of one of the players.

* * *

Teor 2. In a flat area we place columns some next to other one, hermetically joined the column i with i-1 and i+1 (and only with them), such that the first one and the last one also stick. There stay two separated regions, a nursery, which we can fill with water without it happening to other one.

* * *

Teor 3: In a square pond, we wave the water (gently) and at least a point will not move (or the waters are opened).

Warning: the next paragraphs contain the demonstration. It can be omitted in the first, second, third one... reading. The simbolito √ in front of some numbers 2 refers to 'root'. The html is not math-friendly.

Let's see: if any point displaced at least a distance h, let's cover the surface with a network of triangles of diameter d minor to h (we will say in the end who are h and d).

Let's paint the apexes of red if the coordinate x changed h / √ 2 or more. If not, we paint it of green (the coordinate and it changed h / √ 2 or more).

the way is only an indicative, it might be any other

There will stay a way of red apexes or one of green (I replaced a triangle by a column if it has at least two red apexes: it has a dike, or the water happens). Let's suppose that the way is red, it does not matter. It begins in to *, and the coordinate x increased at least h / √ 2. It comes to b *, where it diminished at least h / √ 2. Then, in some moment, a change of signs took place: in two apexes of the same triangle 2 jumped at least 2 h / √ (that is major to h).

Now, we need a little analysis to say who are h and d:

If T is the transformation that waves the water, and the norm euclídea of T (x, y) - (x, y) it is not annulled, is bigger than one h (since it is continuous).

The images of two points of the square for T will be over a distance minor than h if they were over a distance minor to one d' (since T uniformly continuous).

Then, if d it is minor to d', there are two apexes of the same triangle where the function jumps more than h Ridiculously!

* * *

These three big theorems are equivalent between themselves. It is not difficult to demonstrate any more or less general version once one has the idea.

On them, let's say that the first one identifies it to Jordan. Gauss used it several decades earlier, without demonstrating, considering it to be 'clear'.

Brouwer, intuicionista, was pushing the 'traditional' mathematics back, but his theorem of fixed point demonstrated to be of big utility in the classic mathematics. An application that it did was to generalize that of Jordan to Rn, changing curves into hypersurfaces. It seems that Poincaré knew by intuition it: his idea was that if one was throwing sugar in a cup of coffee and it was stirred, some granite in the surface was not changing place (his theorem ergódico is one of so many people ramifications of this so simple idea).

The Hex was invented by Nash (a few years earlier Piet Hein had invented it). The relation of this game with the theorem of Jordan is clear, it is not difficult to prove the equivalence. With Brouwer it is more difficult, but it goes out: the existence of a balance of Nash is a direct consequence of this theorem (and it cost him a Nobel Prize). For another implication, it is necessary only to check what we did above, an idea of David Gale.

* * *

The idea that connects them is that the water has no form, but it reveals to us the local form that it occupies. Serve as moral, or better that it serves as base for the demonstration of some another theorem.

* * *

(special for the Mathematical, organized Carnival this time for Tito Eliatron)

Watch 90210 S02E14 Girl Fight free

1544. - Aumann and the poker

Last year we had a strange meeting with Aumann: approximately twenty teachers of economic and exact, and approximately fifty agents of the mossad around. There was a question that I did not cheer up to rise to him, and I imagine which his answer would have been.

More than fifty years behind, the Israeli police closed a gambling den in Jerusalem, where one was playing the poker for silver, and the defense called it Aumann to testify. To testify on what? That the poker is not a gambling game, but of skill, and therefore, it was not punished by the law. But despite his mathematical defense, the judge condemned the timberos.

Kalai was telling that then Aumann met the judge, and he asked him for his mistake. His answer would have been that in these places the people lose quite, ruining his families.

Kalai argues that the judge is right. Re-formulating his argument, the laws point at an ideal, and the bets games are harmful to this social ideal (also he quotes a variant of the argument, the judge had to discard Aumann, appealing to the Misnah: the players must not bear witness since they do not contribute to the creation of the world!)

* * *

It had in mind the history, and the post who linkeo was reminding to me something that happened to me at the beginning of '90. Vívía with a few friends, we were all students, and we were buying many things in a municipal fair that we had close (on Santa Fe, under the bridge of Pacific Ocean). In one of the positions, a pair of old men was playing the chess, and when it was going was doing some party with them, according to the time that it had, or his clientele.

But one day, there was no any more board: the municipal inspectors appeared one day, and they left to them a cartel that remembered an old ordinance that was prohibiting the gambling games...

* * *

It had never counted this anecdote, I suspect that Aumann would be still laughing at us. It is not a gambling game, with which the strict law is not applied; neither nor were bets of for way, which discards the social ideal after the law.

But I hesitated to ask Aumann if he kept on thinking how he was thinking earlier: that the mistake was unacceptable, because these judges were not obeying the law, but his personal vision of how there had to be the things. I suspect that yes, because this keeps on being his position against the economic salvatajes (in the fund, which there fuck the banks that took risks, they knew that it could happen) which shows a surprising coherence over the course of time.

Download 24 S08E12 Day 8: 3:00 AM - 4:00 AM free

1546. - The relativity of the indexes (II)

Let's explain the mini post of the one of the dawn, at this hour it was not to write much more. Let's define the necessary minimal thing so that the formula is understood.

An investigator published different (je) papers that we can call a1, a2..., an.

Each of them is quoted by himself, his friends, and other investigators, with which we count the number of appointments and see that
there are c1 works that they quote a1, c2 that they quote to a2..., cn
they quote an.

That defines an index of very rapid impact to us to evaluate the quality of the investigator:

c = c1 + c2 +... + cn
(many appointments not always guarantee that he is a good investigator, but very few guarantee to us that it is not very good).

* * *
In 2005, Jorge Hirsch (an Argentine physicist who spent to better life in '70 (*)), introduced the h-index: let's suppose that we arrange the works as the number of appointments, of bigger than minor, and we place below the succession of natural numbers of minor to major:
c1>...> cn
1
Now, we have c1> major or equal to 1, and it will be last j such that cj is major or equal to j (since there are two lists of points, the decreasing one and another flood).

That one is h, the h-index, that it is understood easier saying that there is j papers, each one with j or more appointments.

* * *
Hirsch had already said that h it was climbing like the root of the entire appointments. Now, Redner demonstrates (**) the formula of the previous post:

c = 4h2
Redner analyzes the cases where the quotient √c/2h moves away much of 1, and finds common characteristics in every class of scientists. Very pretty.

* * *
The formula walks well with me (the quotient is 0.98) and with Caffarelli (1.02), so we can make sure that it covers both ends of the quality bogey.

* * *

(*) It Emigrated, it is in California.

(**) It Demonstrates to the physical thing: plotea semilog 255 information. I believe that with the mathscinet thousands might be obtained. Equal, I have fondness to R, believe that it was referee of a paper that we start with Matías in this blog.

1547. - The evolution of the mathematical literature

1660 (in Latin):

London, March, 1668

Dear Fulanitus: the previous year I received a Menganeus letter dated in August, 1664, where it receives geometrically the extract of the movement of the fluid bodies. With big pleasure I verify that it obtains the same results to which I had already come approximately twelve years earlier, and I am useful now to communicate them to him.

* * *

1760 (in French):

Note presented in the Academy of Sciences of Paris, pair Monsieur Fou L'Anneaux et Monsieur Mainganau.

In this note we analyze the movement of a fluid in case it remains in absolute rest (and we will demonstrate that it does not move), or that it is in rest as regards a receptacle that contains it but that translada (we will demonstrate that translada with him). As the remaining cases were already analyzed by Euler and the Bernoulli, we put this way a golden brooch to the theory of the hydraulics and the hidrodinamia.

* * *

1860 (in German)

Herr Doktor Proffessors Vulanner und Menkganniten demonstrated the continuity and difereciabilidad of the flow of a particle inside a fluid and analyzed the distinguishing equation that it satisfies. We will re-write here these way results vectorial.

* * *

1960 (in English)

In the works of Fulanov and Menganiev there was analyzed the probability of which a particle inside a fluid was following a family of curves given inside a space of functions so generally that it includes those of Sobolev, Besov, and Orlicz. Here, we are going to restrict ourselves to a grafo of ten nodes, faced, and the set of discreet ways between his nodes when it is chosen at random and with uniform probability the nearby node to which it will go.

* * *

2060 (in???)

We translate here the last article that Ning came to our hands of Fu-Lan Oh and Meng Ah. We omit the previous definitions, and the demonstration of some of the most used mottoes, since they were published in the journal of certain university of a province that we could not identify in the map.

1548.-The science that the people like

Most of the fauls that are perpetrated in a fóbal party (called football ó soccer in other countries that also take it seriously, and soccer in the countries that do not give him ball) are ambiguous, and there does not exist an objective way of determining who it is the one that "truly" committed it not who the "real" victim is.

Both the fans and the referees often base on a series of signs or tracks to judge the faul situations.

In previous works there were analyzed factors as the color of the T-shirt (Frank et 1988; Tiryaki 2005), previous mistakes (Plessner et 2001), reputation of the team (Jones et 2002), and uproar of the public [hooligans' songs] (Nevill et 2002).

Here, based on different boludeces that linkean the perception of the height to the concepts of force, potency and aggression, the authors argue that the height is one of these signs, and in an ambiguous situation, the faul assumes to the highest (unless it is Palermo, because as it is of Mouth they do not charge from him in against; or that is Ortega against the Dutch archer). This seems explains the tendency of the defenders to run semibent, not to reveal his height, and of step to fell from below the forwards.

They found information that support this hypothesis in the information of the last SEVEN glasses UEFA, SEVEN periods of the German Bundesliga, and the last THREE World cups FIFA, and of two experimental studies.

The Ist strongly recommend this work for publication.

1549. - Carnival

This week they are published posts with mathematical content as part of the second edition Mathematical Carnival. The idea is that they order me the link for mail, or the posteen here, and on Monday I will publish the different contributions.

Closing date: 14/3 (let's write it 3/14, the famous day of pi)

The previous week regretted without having been more active, what we are going to do to him.

1551. - My Non-participation in the 2nd edition of the Mathematical Carnival

Paradoxically, for time questions, I am not going to write a post for this 2nd Edition of the Carnival. The fact is that I am reading the different posts, commenting on them, consulting the authors when I do not understand anything. I find every only participation, that a break is deserved to appreciate it, and added to other questions, I have no time to write anything decent to take part.

I leave them, then, two old men posts mine, in one they can see to what I devote myself; other sums up, in the last paragraph, my look on the history of the science and his publication.

And, as many of you, me like postear problems, to find them, set in the searcher of the blog "problem (it) to". The history of why do I qualify with 1 (one) to those who solve them correctly, it is here.

1552.-2nd Mathematical Carnival 1/2

More than 40 collaborations (for the time being). I hope not to have forgotten none, and if I did it, warn me that I add it immediately.

For the prompt thing, they are divided in two groups, which will be published in simultaneous, and to arrange them better, I classified them under different categories. I believe that every post sent to the Carnival deserves that we take certain time with him, and believe that this way it is facilitated to do a break to continue later.

I made a brief comment of each one, and in many cases I have added links, but I preferred to leave them like comment in the corresponding blogs, and not turn the attention away from here towards third.

Let's start with the parade of that I titled Education and Personal details.

Education

Mathematics, atoms, hair and snots: Sergio brings to us the problems of Fermi, which teach us to do rapid estimations to attack insoluble problems in appearance. The hardware that they use is simple: to extrapolate from reasonable samples, to annotate the quantities between magnitude orders. If one takes it seriously, and it attacks a problem of investigation, the following step, to deduce simple formulae like the laws of Kepler, the period of the pendulum or the law of universal gravitation, it is the analysis adimensional (also it serves to determine the time of cooking of a chicken). And finally, when it has involved functions, the Nirvana: linealizar (or Taylor of order two, never more of that). Since they see, hardware that fit in the portfolio of the lady or the pocket of the gentleman, do not allow to catch them without them, and they be transmitted to his pupils.

You grasp in the sleeve in class of Mathematics: Juan Luis indicates a set of examples to surprise the pupils. For me, the topic of the big numbers is one of the most interesting, for his connection with different fields (algorithms complexity, without going further). My favorite example, to introduce the exponential growth, there are the chains of mail if each one forwards them to ten contacts.

You remain in a square, Construction of an Omnipoliedro with PVC and cañitas of refreshment and Antimagic square. Intense level: Joaquín brings games and constructions over for the classroom. I recognize it: I have zero intuition / handling of the geometry of R3, and except a bucket (thanks to my experience with dice), any other object I it must manipulate a little bit length before 'seeing it'. He would have to practise a little bit with the pvc polyhedrons...

The Fermat room: Manu does a criticism of this movie, and leaves to us the puzzles that appear in her.

A big problem masked by the apparent simplicity of a story: The Beautiful Sleeping one: Manoli leaves also a problem to us, but I believe that his reflections are more important on the education.

We play with Sidon and Golomb: Antonio brings another problem over to explore in the classrooms, with guide of targets, instructions, table in excel, etc.

Carnival of Mathematics II (III Centenary of the Fair of Albacete): Juan brings to us an elementary problem, based on the error of adding two times the same. [On the invitation that it does: it would be loved to the Fair of Albacete! let's arrange the matter of the passages and the accommodation, and there I go ;)]

Method ac for factorizar trinomios on Z Carlos brings a method for factorizar trinomios in Z.

The Simpson: the girls want only to add up Eva presents the chapter of the Simpson (in answer to the sayings of Summer, I am thinking about remembering), and adds a sheet questionnaire so that the pupils should complete.

Personal details

Sixth Sense: Tito leaves a Darwin phrase to us, on the sixth sense that the mathematicians seem to have. It is worth while following that the link that Francis leaves in the comments and reading in more should detail the autobiography.

The formula of Of Moivre: Jesus Soto brings to us the relation between the formula of Euler and that Of Moivre (that is previous). In fact, Roger Cotes got them into the way, finding the formula that today we call of Euler. I can only repeat something on that I commented one day: thousands of things it did Euler, which take foreign names; and the few ones that take his name, it them did other before him!

Sofía Kovalevskaya y Cauchy: E. Gracián contributes with another two posts, the biographies of two mathematicians who also join in the name of the theorem of existence for equations basic in partial derivatives.

The famous number Pi: Ann Maria elects this number as an axis of a series of posts, worth topic for a Carnival that closes 14/3. I keep on believing, equally, that we-hispanoamérica - he should celebrate it on July 22.

The order of the factors sometimes alters the product: Migui gets with the not conmutatividad of the operations, and quotes examples of those that it is worth while: kitchen recipes, to turn a bucket Rubik, to cross a street with semaphore, and many others.

To study mathematics: and why not?: Javier reflects on the mathematics careers. His motivation is the fall of the registration. For these sides also a mathematician is difficult to find without work (still the advanced pupils usually obtain something, although it usually enter a cycle that prevents them from being received because they have no time to dedicate him to the career, and it is not also so many urgency for be receiving since they already have work). Also there is very true the topic of the facility of the calculations, or the numbers handling, although when I say to what I devote myself, I do not have the same problem (as they can see in the first link of my 'non-participation' in the carnival...) . Nevertheless, the final point on Later what do I do? it depends too much of individual capacities that do not belong to the career (capacity of synthesis, flexibility in the reasoning, modeling of different situations, capacity of planning). In fact, having them, it is still difficult to mention an employment where I reached with this; that's why the objections of some comments are very worthy of attention.

Nevertheless, in this that I add, am not giving an account not to study mathematics, and coincide with the general idea that raises the same title of the post: to study mathematics: and why not?

Crisis times, qualifications with future. Do matemátic (and II): Luis supports Javier's post.

The Problem of the First Digit: Beleragor speaks to us about the distribution of the first digit of the natural numbers. He did not know that Gauss was surmising the Benford law, but it would not be strange in anybody that it was manipulating logarithmic stage often (that is, in the fund, what hides behind this law).

Synthetic thought: Antonio reflects on the artificial intelligence and the Test of Turing. Whenever I see this topic, I wonder if Turing will have imagined the current situation, where to leave a comment in a blog, to register in a place, and so many other cases, we must demonstrate that we are not a machine route a captcha. A good source, without many mathematics, for this topic, is the book The Eye of the Mind, of Dennett and Hofstadter.

Teaching to Think: Silvia brings to us an acquaintance pseudo history of the science.

Famous appointments on Pi Eva he adds appointments on pi of different epochs.

Being about the border blogosférica: Edition Day Pi: Javier brings to us, between other things, an excellent article of Bob Palais. The truth, even the perimeter suits (using I remove instead of the diameter). The truth, the only formula that would turn out to be harmed, is the one that says to us that the gravity is pi to the square... but there are small those who know it, so it would not be a big disadvantage!

(in fact, the post that it was going to prepare was treating exactly about that: g=pi2... it will stay for another opportunity!)

My not participation in the 2nd Mathematical Carnival: For time questions, could not write a decent post, and I preferred linkear two old men posts to which I have certain affection to them.

Triple Teselación in Masjid Negara: I close the list with Rafael, next host of the Carnival, with a post that does not deserve words, but to enjoy the images.

1553.-2nd Mathematical Carnival 2/2

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!