Last Tuesday I left to you a tenth mathematics initiated by the one who writes and finished off by a friend in his blog Of tops and subsoils. Well, today, birthday of the one that speaks to you, I bring to you the same beginning but with fianl alternative, finished off after my own autopass.
I hope that it should be of your taste.

Derivative and integral
there are spirit and extract,
mathematician attends
of the Natural sciences.
If you want to know if you cost
for the exact sciences,
it derives perfectly
and it integrates with devotion.
Or with the demon you compromise
so diabolical treachery.

Last March 15 there took place the Second Edition of the Carnival of Mathematics, which so well has been organized by Juan de Mairena [v.2.71828]. The summary of released articles, with personalized comment of each of them, it is possible to find in two parts: Part 1 and Part 2. You recominedo earnestly that you pass a little bit reading both summaries and investigating a little for the magnificent blogs that have taken part with almost 50 contributions.
But we are going to make use of this entry to announce to you that we already have dates and host for the Third Edition. in this occasion we travel to Chile with the blog Dynamic Geometry. During the week from April 12 until April 18 (from Monday until Sunday), all those articles they will be able to publish that queráis on any subject-matter related to the Mathematics. On Monday, the 19th of April (third Monday of April), the blog host will publish the earnings summary. You can see a little more of information in the Announcement that has been done from Dynamic Geometry.
Only I can only be grateful to all those that you keep on informing in this initiative and, which they do not inform, up to cheer you to try to write anything to spread the Mathematics and to extract them of the fund of the drawer.

… of between the ancient mathematicians, which more has influenced me has been Euler, principally because Euler did something that no other mathematician of his size did. He told how he obtained his results, and I am deeply interested in this. And com has to do my interest to solve problems.

George Polya, route Division by Zero.
The Hungarian mathematician Polya pronounced this phrase in an interview that did to him in his ninetieth anniversary (90 years) and that can be in The Two-Year College Mathematics Journal, Vol. 10, No. 1 (Seed drill., 1979), pp. 13-19.
The truth is that I cannot agree any more with Polya, since, at least in my classes, I try to teach my pupils to solve all kinds of problems, and not to that two or three are learned of memory. More important comprehension is the process and to apply it well, that to realize the calculations correctly and to hand (at least in an examination).
And you? what do you think?

Today, On March 14, or as the Americans would say 3/14, it is celebrated the day of π. So I leave a small video to you with a cancioncilla on this number. certainly, be attentive to the deifying end.

Not long ago I became a fan of one of these groups of the Facebook. But in this occasion I did it with all those of the law. The group in question calls the Fact is that I am of letters …: and I of numbers and I can write!. Really one of the motives for which I initiated the Carnival of Mathematics was so that the phrase with which it begins in title of the group, was beginning disappearing of the language of some persons.
And to illustrate it is done, there left to you a fragment of the movie of Woody Allen of the year 2000 Dodgers of half a hair, and that I saw in the Prohibited blog bringing in to that one who does not know mathematics.

So that then they say that the broken ones do not serve for anything, and if not, that say it to this dodger. I am going to put the tag humor, but because the movie admits it, but also that of mathematical incompetences.

Since not, we are not going to speak about this type bodies, but about the mathematical Body concept, that is to say, of algebraic structures. In particular, we are going to center on the numerical bodies.
In principle, a body is an algebraic structure on a set of elements (commonly called things) in that we have defined 2 types of operations: the sum (+) and the product (*). In principle, these operations do not have porqué to be what we usually understand for sum and product, but if we center on the set of the numbers, we can think that there are nustras well-known basic arithmetical operations.
But skylight, it is not enough to only have the operations, but these must to fulfill a series of properties. We are going to fix ideas. A set (X, +, *) (that is to say, a set and his 2 operations) it is a body when the following properties are fulfilled:

With these properties, and we are already going to center in the Numbers the smallest body that can be, with the sum and the habitual product (and this is tremendously important), it is the Body of the Rational Numbers.
In the following level, the body most used by all is: the Body of the Real Numbers. We even can spread a little more and come to the Body of the Complex Numbers. Really the latter set, that of the complexes, is an extension of the real numbers so that the RADICAL operation (to take root of any index) has sense. Basically, this body arises of setting off of (R 2, +), that is to say, the plane with the habitual sum of vectors, and there is invented an operation, called a product (*), that fulfills all the properties of body. East operation acts of the following form: (to, b) * (c, d) = (ac-bd, ad+bc) And if we write this operation between complex numbers in his habitual form, it proves that (a+bi) * (c+di) =ac-bd + (ad+bc) i
to include like authorized number the imaginary unit i = -1 and to work with him, as if of the second coordinate it was talking each other.
But: might we extend, of any form, the concept of complex number any dimension more? Really yes one can. In fact, we can speak about the Cuaterniones, which are to the Complexes, what these to the real ones. But the problem that arises is that this set does not have body structure. And he lacks her, not for his own definition, but because it is impossible that it has it, since somewhere near 1863, some Weierstrass proved an interesting fact he is the acquaintance like Final Theorem of the Arithmetic, who affirms that for n≥3 it is impossible to provide the additive group R n with a product operation (*) so that (R n, +, *) it has body structure. In other words, that for much that we get into debt, we are not going to be able to find a definition of the product that it extends to the product of complex numbers and that fulfills all the previously described properties of Body.
To conclude, we are going to turn a little back, there where he was speaking of

the smallest body that can be…

If we forget of the operations sum and standard product, the smallest body that it is possible to construct with numbers one usually calls Z2 and it is formed by 2 neutral elements: {0,1}. The operations it adds up and product they are defined as it continues:

• SUM:
• 0+0=0
• 0+1=1+0=1
• 1+1=0
• PRODUCT
• 0*0=0
• 0*1=1*0=0
• 1*1=1

Basically the operations standard are, but inside the Modular Arithmetic, where, in this particular case, 0=2=4=6 =…, 1=3=5=7 =…
Anyway, that I believe that we have already got tired of speaking about bodies. If you have not liked the content of this article, at least I wait that you should have enjoyed the image incial. Certainly: have you seen the girl who exists after the spiral?.

I have regretted without having advanced deeply at least the sufficient thing as to understand something of the big fundamental beginning of the mathematics, since the men who dominate them seem to possess a sixth sense.

Charles Darwin Vía Boletín 217 (PDF) of the RSME.
It has paid me powerfully the attention this appointment, more if it fits, when 2010 is the year of the biodiversity. Anyway, I do not know if to agree completely with mister Darwin, because, as much as to have a sixth sense… seems slightly exaggerated to me. Of course, intuition I believe that the mathematicians do not lack. Do you think as I?

Since it has already happened one month since there took place the First Edition of the Carnival of Mathematics here in

It does some time I registered in Formspring.me and lately I have received several questions on the mathematics education, why they turn out to be so boring to us, or the cause of the typical distaste to the same ones. So I have decided to tell you what was what motivated me to study mathematics and to live of them.
Let’s begin from the beginning (not, to Big Bang, no; a little later). In my house I have always heard all my life speaking about Mathematics: not in vain my parents are both mathematicians. For this motive since I have use of reason the numbers always turned out to be familiar to me. It might be said that instead of red and white globules, for my veins they cover rational and irrational numbers.
For ages the numbers have attracted me. In fact, one of my favorite games when scarcely he was 4 years old was to add the digits of the registrations of the cars when he was traveling with my father. Even when it was at home, it was playing at putting mathematics examinations in a slate, likewise he was listening to my parents to comment on what they were doing in his classes.
Later there came the puzzles of ingenuity, these of the truths or the outstanding figures in poems. Even some ingenious phrase on the mathematics. Little by little, and without realizing, I was beginning wanting to be a mathematician.
Little later, in the school, already it was aiming at ways in mathematics. As example, a pair of anecdotes. In sixth of primary, my teacher, a major master of the old woman (good, even more ancient) school, was correcting the problems for the system of the majority, that is to say, he was asking about the results that we had obtained, and the fact that more people should have it, this had to be the correct one. Everything was going perfectly, until one day I was the minority, and skylight, that did not matter for me. The teacher said that my result, to the being (for major derision) the only one that had obtained it (the rest of my partners obtained all the same one), had to be erroneous and I was located that it was checking again. So I got up and said to the teacher that it had it well and that if he wanted it was solving it in the slate. He accepted angry enough, I went out, solved it and, before his porpia puzzlement (of course, and the anger of my partners) it admitted that all the rest had it badly and only I well.
A pair of years later, in eighth (2nd of THAT today) another teacher (physicist, for more signs) asked us that how much was costing 1 divided one between 0. I raised the hand and said that this operation cannot be realized. The teacher (with a little of sarcasm) said to me that it was badly and that the result was infinite. The guffaws of my partners it was brutal. But that did not stop me and I said to him, that if that was true, of that time since 2 divided between 0 also would be infintio it was deduced that 1 equal age to 2. The face of decomposition that it never put will forget me, but if I gained 2 things: one was that of not having to do (together with another friend and partner) more final mathematics examinations this course, and two, I won a big admirer, since this teacher, whenever it sees me, greets me very ardently and with many happiness, which I also return it to him since it demonstrated to me that a teacher can be wrong and be able to rectify before a pupil.
Anyway, that not to be heavier, during the institute, my relation with the mathematics kept on being definitely increasing, I even gained some contest of games of ingenuity with another good partner who today tmabién is mathematical. But perhaps what more impressed me was my teacher of 3rd of BUP (1st of Baccalaureate today). She was a very peculiar person, old and passionate professor of the Mathematics. And that could transmit it to me. After every small hook of a class, it was always telling us something completely distitnto, but related to what we were giving. Sometimes his parentheses lasted 2 or 3 days, but it was always interesting to see the biggest network of interactions that are the Mathematics.
Finalemente I decided to study Mathematics and, of course, I never repented of my election. True it is that they were not given me completely badly, but that does not remove that he will dedicate a big effort to the career. After her, I decided for the investigation in mathematics and this yes that it is already the maximum thing. To solve a problem that nobody earlier had done it ever, is an indescribable experience (not, it is not like an orgasm). And here you have me today, teaching mathematics in the University of Sevill to and her spreading of the best way that I know in this small personal corner that it is

The miracle of the validity of the language of the mathematics for the formulation of the laws of the physics is a wonderful gift that we neither understand we do not even deserve. We should be grateful for it and to trust that it will keep on being valid in the future investigation and that it will spread, for good or for evil, for our pleasure, even if also it does it for our puzzlement, to wide branches of the knowledge.

Eugene Paul WignerVía Boletín 204 (PDF) of the RSME.
Really it is fascinating to realize how a little so abstract and formal like the mathematical language, which we already saw that he was looking for the relation between the forms, in the end it is always possible to fit in the physical reality, well across distinguishing equations, as in case of the overhead power cable or the Second Law of Kepler, good across the simple geometry.
And do you say yet that the miracles do not exist?