The office of the teacher Enigma (10)

Our today protagonists travel on board of a rocket in the direction of the Moon. After a series of fortunes, and when they are at a distance of 240.000 km of the terrestrial base, they prepare to realize the maneuver of investment of the rocket, which will allow them to brake his inevitable fall. Before proceeding to light the retrorockets, they must make to rotate the ship, placing the bow looking towards the Earth. In this moment, it is possible to listen from the control of the mission:
"Earth to lunar rocket: prepared to start the side reactor... Ten seconds are missing... nine... eight... seven... six... five... four... three... two... one... ZERO."
The rocket begins to rotate and turns to listen for the radio:
"Attention! Prepared to extinguish the side reactor... Ten seconds are missing... nine... eight... seven... six... five... four... three... two... one... ZERO."
From the rocket the following message is sent to the Earth:
"Lunar rocket to Earth: the investment maneuver...: it has gone out to the perfection! we are in the correct position to reduce progressively the speed and to land on the moon safely."
About what marvels are we speaking and which or what are the blunders? Luck and for it!

The office of the teacher Enigma (10): Solution

Since the day has come, darlings and sapientísimos, sharp and shrewd readership. I have been surprised very pleasantly with the answers that you have provided to the teacher Enigma.
Well, let's go on parts. The extract corresponds to a few vignettes of a cómic of Clink, in particular the alumnus "we Have trodden on the Moon", of not so magisterial one (científicamente speaking) Hergé. Congratulations to those that you gave in the nail!
Let's go now with the physics. In this also you have pointed the blunder many of you. Really, to use only one side rocket is not effective at all if he wants to make to rotate one or to turn to the rocket and that stops when it has turned 180th. Remember that the movement of an object in the ambience is quite different from the one that he would execute in absence of the same one, in the gap of the space, where any aerodynamics of the fuselages turn out to be completely useless. And so, to produce the rotation of the ship (as they try in the cómic, that is to say, putting the bow looking towards the Earth) of our friends, at least, two side reactors are needed. There must be wings because if his action lines were happening for the center of gravity of the ship they would not also produce a movement rotacional (this is a good opportunity so that you revise Newton's laws, if it is that it does not offend you too much). Abounding slightly more in the topic, in case only one side rocket was managing to make to rotate to the Clink ship, this rotation would be supported indefinitely, while another opposite force was not opposed. That's why more than one side rocket is needed, to be able to brake the rotation in the suitable moment.
As curious note I can say to you that the spatial ferry that the NASA uses to realize maneuvers in the space is equipped along all his fuselage neither more nor less than with 44 microrockets that allow him to move and do corrections in his displacements. The same way, the rucksacks with which there are decked the astronauts who execute spatial walks out of the ship, have 24 propellents that work expelling gaseous nitrogen.
Finally, let's discuss a little some question aimed in some of the comments. The 240.000 km distance to which one alludes in the post is not expressed of incorrect form that, that is to say, there are no miles, but really km. Now then: does turn out to be reasonable to realize the maneuver of change of sense or investment of the rocket at similar distance of the Earth? The truth is that the movement of a ship in the direction of the Moon has some complexities that do not come to story here now, but yes that I would like saying some things.

Along the Hergé cómic, it is seen that sometimes the protagonists activate and deactivate the principal propellents of the ship, without much felt. This does that the rocket acquires accelerations that produce very curious effects inside the same one. A rocket that we were throwing in direction of the Moon would be "falling down" almost all the time towards the Earth, since this one never to stop exercising his enormous gravitational influence. Nevertheless, as it is approaching the Moon, the force exercised by the Earth is diminishing and, on the other hand, the exercised one by the Moon is increasing increasingly. When the rocket reaches a distance to the Moon approximately equal to the ninth part of which it separates from the Earth both bodies (Earth and Moon) they will exercise the same gravitational pull on that one, with which the rocket will begin to "fall down" towards the Moon. One might feel touched of saying that it must be in this point where the rocket must invest his sense and begin to brake, but this is neither definitely necessary nor essential and, therefore, he does not constitute a blunder in strict sense. One can travel towards the Moon at a madmen's, extremely high speed (I remind to you again that our maddened friends accelerate the ship sometimes, making her gain speed) and begin the braking process to the beast and at the distance that it avenges in desire, although it is not too reasonable.
As for the topic of the delay of the signs due to the distance to the Earth, he is not a blunder either. It is supposed that the personnel of the center of control knows this and can move forward or slow down the messages to compensate.

What would happen if the force of the gravity was increasing with the distance?

All that you have studied one day little physics you will not have problem too much in remembering the called law of the universal gravitation, enunciated by Isaac Newton any more than 300 years ago and published in 1687 in his famous ones It "Begins", perhaps the most influential scientific work of the history of the humanity. The legend that he accompanies to this law (certainly, that for only a few days is already not a legend, since there is written steadfastness of which it happened really) tells that it occurred to Newton while he was listening to the noise of an apple after there rushed to the soil from a branch of his tree mother (one notice the party indexes to "Incarnation"). He wondered what could be the force that could explain the fall of the apple and the movement of the Moon about the Earth. And it found it. A simple, beautiful law. Expressed briefly he was coming to affirm that between two any bodies of the universe an attractive force existed, an action over a distance that it was increasing proportionally with the values of the masses of both bodies but that, on the other hand, was diminishing in inverse reason with the square of the distance that was separating them.

This force had the same nature, already out between the apple and the Earth or between this one and the Moon. All the bodies of the universe were moving following orbits determined by the law of the universal gravitation. It was proper Newton who deduced how there would be the geometric forms of the orbits or trajectories that should describe the planets, asteroids and comets about the Sun or also an apple dropped close to the terrestrial surface, as well as if it was thrown by different impulses from the top of a mountain. The above mentioned trajectories could be only three classes: parables and hyperbolas (open curves) and ellipses (closed curves). The above mentioned, that is to say, that the orbits were elliptical in case of the planets and the Sun had been already discovered by Johannes Kepler in 1609, when it enunciated the first two laws of the planetary movement that take his name, basing for his deduction on the precise remarks carried out by the Danish astronomer Tycho Brahe. In the first one of them, Kepler was establishing that all the planets of the solar system were moving about the Sun following ways with elliptical form, being always the Sun placed in one of two foci of the above-mentioned curve. The circumference was a particular case of the ellipse, that one in which both foci were coinciding with the same point (the center of the circumference). Nine years later, in 1618, Kepler would complete his work with the statement of a third law. This one establishes that the time that uses every planet in giving a finished return about the Sun depends on the mutual distance between them. More exactly: the square of the period of rotation is straight proportional to the bucket of the biggest semiaxis of the orbit. This way, the duration of the years in other planets more removed from the Sun than the Earth is every time major as his distance increases our star. On the other hand, Mercury (88 days) and Venus (225 days) they have years shorter than the terrestrial ones.

Like already handyman, Johannes Kepler discovered his laws of empirical form, based on extraordinarily precise astronomical remarks on that epoch. Nevertheless, it had not even idea of which age the deep reason in which they were resting his discoveries, that is to say, did not know the mathematical form that had to have the interaction force between the Sun and the planets. So in the year 1684 he decided to come to Newton, who informed him almost immediately that the mysterious force for that Kepler was looking was verifying the famous law of the inverse one of the square. It was doing years that Newton was supporting a series of sour discussions and philosophical battles with Robert Hooke. Apparently, the last one had proposed to him to Newton the idea of the change of the force with the inverse one of the square of the distance and had suggested him the resolution of the mathematical problem. Newton never recognized the value and the ideas of Hooke.

Although I do not know and (still) I have not managed to find the original sources, it seems that the first ideas of Hooke on the concrete form of the law of the gravitational force supposed that this one was similar to the exercised one by a wharf on a body subject to him for an end. This way, he was imagining the Earth joined by a gigantic wharf to the Sun. In 1660, Hooke had thought that the above mentioned flexible force was proportional to the stretching of the wharf. How in case of a planet and the Sun was the stretching of the wharf major major all that was turning out to be the distance between two stars, the gravity was increasing with the distance instead of diminishing with the square of this one, as we know nowadays.

But perhaps you are wondering how it is possible that there could occur to someone similar idea, an idea seemingly frenzied and arisen from the boldest history of science fiction, worthy of the most creative movie of the genre in the last years (separate, clear Roland Emmerich). If you have been attentive to the dates, you will have noticed that from 1609, date of the first two laws of Kepler, already it was known too that the planetary orbits were elliptical. How then was anybody daring to propose a law of the gravitation so different from the newtoniana (still not known for then)? Since the reason was very simple. The flexible gravitational force suggested by Hooke was predicting also elliptical orbits for the planets. In effect, since well you will have learned also in the books of basic physics, when a body is subject to a force of flexible type like the given one by the law of Hooke, and whenever the movement is in only one dimension, the trajectory continued by the above mentioned body will be a straight line and the movement receives the name of harmonic simply. On the other hand, if the trajectory that continues the body is contained in a plane, as it is the case of the Earth or any other planet about the Sun, then what is had is a superposition of two simple harmonic movements, perpendicular both between themselves. When these two simple harmonic movements get together there arises an ellipse as trajectory (other well-known different combinations exist as curved of Lissajous, but they do not come to story now). Do you consider now Hooke a senseless one? No, truth? Well, since perhaps with what I am going to tell you next your opinion change.

The truth is that the law of gravitation suggested originally by Hooke (I have already told you that later he would rectify himself and would suggest to Newton an inverse law with the square of the distance) is not coherent with the Kepler laws any more than in the elliptical character of the orbits. Why? For several reasons. The first one is that when the movement equations are solved the first contradiction arises and this one is not different that, in contrast to what Kepler was affirming, now the Sun is already not in one of the foci of the ellipse, but in the center of the same one. The second one, and more serious if it fits, has to do with the third Kepler law. Really, if one day you have deduced this law supposing an approach of circular orbit and using the law of universal gravitation together with the expression of the centripetal force, you have only to carry out a calculation exactly equally but replacing the law of force of Newton with that of Hooke. You will verify immediately that now the time that takes the planet in describing a return about the Sun it is always the same one, independently of the distance that it separates from the star. All the planets would have years of equal duration.

And this way, this way so elegant and effective the science works. A phenomenon is observed, it is experienced (if one can), there is prepared a theoretical - mathematical model who explains the remarks and potentially observable new phenomena are predicted. If these phenomena are not explained by the proposed theoretical model, this one gives in and one looks for one that does it. Hooke was a scientist of volume and loin. He proposed his theory. It saw that this one was fitting to some of the remarks but, on the other hand, it was contradicting others already verified by other means (the Kepler laws, in this case). This way, then, it directed his efforts towards another more guessed right model and, consistently, more next to the truth. Some voluntary pseudoscience that makes it better?

Download The Amazing Race S16E05 I Think We're Fighting the Germans, Right? online

In all the drugstores they were saying to me that it should veto, there are no suppositories for similar eyelet

Dedication: For Elías, who very nicely gave me the cómic from which I have extracted similar adventure and with which I enjoyed a good moment.

Clark Kent visits in prison Lex Luthor with the intention of doing an interview to him for Daily Planet. But, once there, it meets that the plans of the supervillain are not different that to escape and to scheme a diabolical plan to finish once and for all with his archenemy: Superman.
The prison is full of types of bad kind. Between them, the very special one, it is causing an authentic massacre, triumphing with everything and with all that it is to his step and that are opposed to his advance. It is a question of "the Parasite", a being capable to absorb energy, the superpowers and the intelligence of any that one which it manages to touch.
In a given moment, Lex Luthor begins to shoot him with a firearm. Immediately, Clark Kent realizes that something strange happens:
- The bullets do not stop it! It is turning the kinetic energy into more mass!
- You are right! - Luthor answers.
In spite of this serious mishap, the bullets rain continues incessantly. Until after a little bit:
- Him the energy is choking! [...]
- My bullets have had to of inclining the scales! It has become too massive to support its own weight.

Well: what do we have here? Nothing more and neither more nor less than a new adventure of superheroes and supervillains of cómic ready to defy the laws of the physics. In this occasion, the thing starts well, but it finishes regrettably badly. Let's see it.

Our horrifying bug, the Parasite, with this aspect of bigheaded slug and indented which lamprey, does not have in better what using his time than in absorbing the kinetic energy of the bullets that fall down on his purple corpachón. You know many of you that the kinetic energy is that that they possess the bodies in reason of his speed. In physics, it is possible to calculate multiplying half of the mass of the body by the square of his speed. Well, if we give them to the bullets that a few values go out of the weapon of Lex Luthor more that generous so much for his masses as his speeds of, we say, 40 grams and 1000 m/s, respectively, at once appreciates that every bullet possesses a kinetic energy of 20.000 joules. This can look like an enormous energy quantity and certainly it it is, especially if it impresses you in the face, in a foot or in any another more sensitive and delicate part of your delicate anatomy. Nevertheless, to the Parasite him mola mallet. Moreover, apparently, all the more better kinetic energy, since this helps him to transform it into mass of its own body and be bigger and more fear gets for the head.

Now then: does turn out to be commendable to turn energy into mass? Since I have not left any more remedy than it to allow. Yes, one can. In fact, m was Albert Einstein who established of quantitative form the equivalence between mass and energy, across his most famous equation E = c2. This expression affirms (and his validity has been confirmed in infinity of occasions, some of them of unlucky memory) that the matter and the energy are, in fact, the same thing. The smallest matter quantities can give place to enormous energy quantities, and quite through the fault of the value of the speed of the light (her c in the previous equation, which also is raised to the square). The mass conversion in energy we see it every day in the nuclear power plants, where the fuel serves to supply partially of electric power the hearths. In the detonations of nuclear explosives identical process takes place, with the proviso of which the energy liberation is not controlled, as it happens in the nuclear reactors. On the other hand, the inverse process, this is the energy conversion in mass, it is usually more difficult enough to manage. Where can we attend this process? Since it usually happens often in the big particle accelerators, where you do of these they make clash at enormous speeds, producing the generation of new particles at the expense of the kinetic energy that the first ones were taking initially. You will wonder, then, where the snag is with our protagonists, the Parasite and Lex Luthor leave to me that I explained it to you.

Anyone that tries to change in the "boutique" of the energy, kinetic energy for mass, is not going to meet reductions precisely. There is always going to cost him the same, that is to say, a price given irremediably by Einstein's equation. This way, replacing in the value of E the quantity of 20.000 joules that had every bullet of those that the Luthor weapon was shooting and clearing the value of m, it is had that this is approximately 0,22 billionth ones of kilogram (the physicists we call the kilogram billionth ones with the nice name of nanograms). What means this? You can find out it yourselves easily. It means that so that the mass of the Parasite increases in only a miserable gram 4500 have to fall down on his body neither more nor less than millions of bullets. In what case does similar Lex Luthor take bullets quantity? Moreover: how does he support the weight of the same ones, if this one reaches 180.000 tons? (remember that every bullet was weighing 40 grams).

And above, the very nice one goes and says after a little bit that his bullets are inclining the scales, that the Parasite has absorbed so many people that his weight is superior to the one that he can support. Luthor, you are pasao, the law Sinde has fucked the quijotera to you. Let's leave the closing webs aside for better occasion and centrémonos in the last affirmation of the “more brilliant genius of all the times”. That you know this blog from the beginning you know the incredible law of the square - bucket or law of the scale. In those primerísimos posts it was telling you that a living being, an animal or a person cannot grow up to an arbitrary size because then he might not support his own weight and this was happening as soon as the relative force was reaching an equal value to the unit. Well, if we grant him to the Parasite a value of 3 for the relative force when it possesses his normal size, that is to say, the force that is capable of supporting his corporal structure is the triple of his weight, Luthor of that time will be right when the volume of the abominable being absorbs - energía-cinética 27 increases in a factor or, what is the same, his mass makes 27 times major to itself. Consequently, and assuming 100 kg mass for the Parasite when this one still has not assimilated suppository of any lead, Lex Luthor will need to introduce for the eyelet the not despicable at all number of 11.700 trillion bullets …

Source: All Star Superman, by Grant Morrison + Frank Quitely, Planet Of Agostini, 2009.

Inventories in the third phase

Lasers, positrónicos, x-rays, Y, Z, alpha, beta, gamma and all the letters of the Latin and Greek alphabets. The most deadly weapon that could imagine has happened for the big screen and always with devastating effects on his victims. A few times, simply stunning like bad minor, in other occasions limiting his targets to ashes, steam or even her not at all, pure energy.
We have attended scenes like that in so much occasions that practically we assume that to limit to dust a human being is a more or less simple task, without much ado requests to be arranged of the suitable weapon. But, let's reflect a little on this question. Let's see, I believe that you all will agree with me in whom a human body has solid appearance, although in the fund a good percentage of our body is a water, but finally we can admit that we behave neither like a nor liquid in strict sense either like a gas. At least, that I know, I have never seen a person adapting his form to that of a receptacle in which it has got. Has anybody ever seen a person who is canned, bottled or shut up inside a balloon of fair, of those that are bought to the children?
Well, once agreed in this (although I know that someone will always appear to discuss it), let's think a little about what supposes from the physical point of view a situation as described more above, that is to say, we have a solid body and transform it into liquid, in gas or simply we limit it to pure energy, according to the bad milk of our armament. In physics we call to these situations changes of phase or of the state and they always need an energy exchange. When one tries to do that a physical body that finds initially in solid phase pass to turn into liquid is necessary to bring him heat. And this heat or thermal energy that is given him must be sufficient at first to raise the temperature of the above mentioned body up to the temperature in which there takes place the phase change (in our case, it is named a merger temperature). But there it does not finish the process since as soon as the melting point was reached it is essential to contribute a quantity of additional energy named latent heat of merger and that is typical of every substance. During the latter process the body temperature remains constant until any of he becomes liquid. If later we kept on contributing heat, what we would obtain would be a new temperature increase, now of the liquid, until the acquaintance as boiling point was reached or, what is the same, that temperature to which there happens a new change of phase (in this case, from liquid to gas) after the familiar supply of the latent heat of vaporization. Summing up, if a solid body is claimed vaporizar it is necessary to raise, first of all, his temperature up to the melting point, next, to carry out the phase change by means of the contribution of the latent heat of merger. Once the whole body is in the liquid state it is necessary to keep on giving heat to raise his temperature up to the boiling point, moment from which the body vaporizará any time the latent vaporization heat is provided to him. In certain particular situations, also it is possible to make to spend a body straight of the solid state to the gaseous one, without happening for the liquid state. This process receives the name of sublimation.

If we try to quantify the previous calorific energies, we must know that these depend in direct proportion of the mass of the body that tries to be struck dead, disintegrate or vaporizar; also, of the nature of the body, that is to say, of the substance itself of which it is formed (this is described across a physical parameter known as specific heat) and, finally, of the change of the temperature to which one wants to submit him. To understand it, I will put a very simple example and clarifier to you. Let's suppose that we have one kilogram of iron that is initially 20 ºC. If we claim vaporizarlo everything, we will have to bring him the sum of four quantities different from heat, namely: to raise his temperature up to his melting point (1803 K) approximately 665.000 joules, to liquefy 289.000 289.000 joules, to take it up to his boiling point (3273 K) 647.000 joules more and, finally, to transform into steam neither more nor less than 6,3 6,3 millions of joules. In whole, almost 8 million joules. If the material was a copper the energy request would be minor, of only approximately 6 million joules and talking each other of lead, only 1 million.
I have to say that the previous quantities do not turn out to be especially high or out of the weapon scope technologically so advanced as those who appear to us in the science fiction movies. Nevertheless, you will agree with me that very little times the above mentioned scenes are usually coherent, since there does not appear by any side the steam to which there has come down the body on which it has gone off. In the opposite case, there might become absorbed original fragrances of armored car or of tank, fragrant extracts of thread of copper ("Cobbrel nº 5"), exotic and sensual perfumes of flowerpot holder of lead (the famous one "eau of plomó" for him and for her), etc.

In other occasions, the phase changes seem to arise for spontaneous generation, and any heat source does not come up, seemingly. It is clear that this is already a superheroes' thing. For example, in the movie Sky High: a school of high flights (Sky High, 2005) one of the boys who is present at the superheroes' school for superheroes' children possesses the amazing superpower to be liquefied or "to melt", as he affirms himself. Now then: where from does the heat necessary for similar skill come? Even more, later to recover his normal solid form: adónde is it going to stop the heat that necessary he must expel from his body? Would it be suitable to be close to him?

Squares, rectangles and more squares

I have always liked very much the mathematics but the courses of the life pushed me towards the physics. I remember especially my first steps in the arithmetical calculation, to do operations at the biggest possible speed and of correct form; the years of baccalaureate, when I experienced the impact of the differential and integral calculus. Unfortunately, on having come to the university, that youth admiration disappeared like the smoke of a cigaret in a gale. The mathematics subjects in the physics career were not what I was waiting for myself: I went so far as to hate the topology, with his open and closed balls, the adhesions and the closing ceremonies; the distinguishing equations did not seem such explained by mouth of my teachers, very much theorem and demonstration and at the time of truth they were the physicists those who had to teach us to obtain the solutions that we were interested in. With the algebra the thing was not very different: vectoriales spaces, dual bases and all that paraphernalia that I have ever never used again in my professional performance like physical.

I suppose that if the previous lines are read by some mathematician one will throw the hands to the head (as always) and he will say to me that if the importance of the rigor, that if this, that if other, but the truth is that I am completely against that the mathematics subjects in the careers that are not the same Mathematics career give them the mathematicians. I try neither to generate debate nor to open any discussion, simply I give my opinion, mistaken or not. End.

Very well, I have got entangled as it is usually habitual in me and I still have not said to you that this post that I write today (not, you have not been wrong of blog) takes as an assignment to take part in an initiative proposed by José Antonio, the author of the marvelous blog Tito Eliatron Dixit, named a Carnival of Mathematics, which target is to spread this so exciting science and that produces so many headaches to million students of the whole world and all the epochs.

For this first edition I have prepared a simple, but nice thing, to return to the origins, to the first steps that happen when they begin studying mathematics in the school. I will center on the geometry and on the arithmetic and will dedicate this entry to the youngest people, which they are of course those who with any more steadfastness need not to feel defrauded, disappointed, for this wonderful human invention that there are the MATHEMATICS.

Many students (even mine in the university), increasingly, unfortunately, remember with difficulty certain expressions as there are the area of a sphere, the volume of a cone, the square of the sum of two numbers and similar things. That of things that one is in an examination...

And if there was some form simple to remember expressions as the previous ones? Since it turns out that yes they are. I am going to tell you, for example, how to remember with help of the geometry the value of the square of the sum of two numbers. That you should have good memory you will remember that this square one can determine addend to the double of the product of both numbers the squares of each of them. But let's see this otherwise. Let's call to and b to the two previous numbers and let's draw a side square (a+b). Let's measure the length to on a horizontal side and let's do the same with a vertical side. Let's plan from each of these points one straight line up to the opposite side of the square. We will have now our original square and in him inscribed a side square to, other of side b, y two sides rectangles to and b. Well, now without much ado that to remember that the area of a square is the square of the value of one of his sides, there is not any more that to add the areas of the two smallest squares and that of two rectangles (a2, b2, ab, ab). And it is already: (a+b) 2 = a2 + b2 + 2ab.

It is possible to make something similar to find the square of the difference of two numbers. In this case, a side square shows to. Next the length measures itself on his perpendicular sides b (we will suppose that b < a) y se trazan dos líneas rectas, igual que en el caso anterior de la suma. Tenemos ahora inscritos dos cuadrados, uno de lado (a-b) y otro de lado b, además de dos rectángulos idénticos de lados (a-b) y b. Lo que queremos es expresar el área del primer cuadrado inscrito (la sombreada en la figura) y esto se puede hacer restando al área del cuadrado de lado a (el más grandote, el que contiene a todos los demás cuadrados y rectángulos, para entendernos) las áreas del cuadrado de lado b y las de los rectángulos de lados (a-b) y b. Total: (a-b)2 = a2 + b2 - 2ab.

Since my teacher's condition does not forget me not for this special occasion, I am going to propose to you, to suggest, to design the necessary geometric method to remember the value of the product of the sum for the difference of two numbers, that is to say, what was saying that "the sum for the difference is the squares difference" ((a+b) (a-b) = a2 - b2).

But the most curious thing comes now. It turns out that the latter expression can take advantage to carry out the calculation of squares of entire numbers of simple form. How is it possible to do this? Very easy. Suppose that you want to know the square of 12. What do you do? Since to add and to reduce to the previous number the necessary quantity so that a number finished in zero is obtained. In this case, there joins and is reduced 2 (let's call this one the magic number). This way, we have 12 + 2 = 14 and 12 - 2 = 10. Next we multiply the obtained numbers (14 * 10 = 140) and to the result we add the square of the magic number (22 = 4). Whole: 140 + 4 =144, which is the looked square of 12. What is the relation between all this and the formulita of the previous paragraph? Attentive: the number to es 12, which we add and remain b (the magic number), having (a+b) and (a-b). Since we want a2 we do not have any more that to clear, with which to the product of the sum for the difference it is only to add to him the square of the magic number: a2 = (a+b) (a-b) + b2.

Have you liked? I hope to make it better in the next edition. Ah, and I apologize to the mathematicians if I have not continued the rigor that so much they love. After all, I am only a physicist...

The (elegant) science of "Incarnation"

It does a pair of months the magazine "Quo" got in touch with me to propose to me to write an article where he should report to his readership the principal scientific errors that were committed in the science fiction movies. Of course, I accepted with enormous taste and illusion. I me started working and sent it to him.
When the definitive version of the article was still not ready and coinciding with the premiere with the movies of the movie of James Cameron, Incarnation, they proposed to me also on the march the second article where he was commenting on the science (good or bad) reported in the cinematographic sensation of the year. And this time I did not also allow to spend the opportunity, since it was very wanting to drive in the tooth to Pandora and to the na'vi.
Some weeks later, two articles have been checked and infografiados marvelously and spectacularly for the team of "Quo". They will see the light in the next number of the magazine, 174, corresponding to March, 2010 and that will be in the kiosks from the next week. Do not get lost it! But that is not quite, so very nicely the magazine has agreed to pre-publish a version online complete of the second one of the articles that I have written for them: "The science of Incarnation". If you puncture in the previous linkage you will be able to read it to yourselves of free form from the proper web page of the magazine.
Finally, it would not be just not to quote the work previous to my friend, companion and alumnus, Iván, who published an article previously on the same topic in his impressive blog Wis Physics. If you compare both versions you will realize the quantity of similarities that exists between them. I have to say in my defense, nevertheless, that I did not know his version even after mine sent the publishers, due to a problem that Iván had with the servant of his web. This way, then, I can only dedicate the article with my biggest admiration and respect.