for those mistakes we all make in Algebra: for my students of 4 º ESO
When we lack vocabulary all students and teachers say "that thing" ; effectively and referred to the unknown in the set of math problems and treaties Algebra as in the book of John the Baptist Tolra , published in Tarragona in 1619 : "Treaty of Art over Arithmetic, Algebra or call rule thing."
The first book of algebra castellan written or published in Valencia in 1552 " First Book of Arithtmetica Algebratica " of Marco Aurel, digitized Virtual Library Miguel de Cervantes and the link can also enjoy:
In the book Marco Aurel said that in the equations of the type: the only solution is x = 1.
How may not give notice that equality is an identity and therefore holds for any value assigned to x?.
need a good notation to clarify the resolution of the equations at that time were algebraists "cosist" and Cervantes in Chapter XV of the second part of Don Quixote algebraist used as a restoration of bones and not an equation solver.
Today in class, Algebra practice more than any other branch of Mathematics, at all levels, blackboards full of x and and - See what e-already practiced in class and besides I want to sing "the girl ye, ye " my students refuse to pronounce it so.
Sometimes a devil is cast into a coefficient changing exercises, a sign, and difficult to solve.
Algebra is the offer made by the devil to the mathematician. The devil said, "I give you this powerful machine, who will answer any question. All you need is to give me your soul leaves the geometry and I will give this wonderful machine. (Michael Atiyah)
Quote found in the preface that Barry Mazur makes an indispensable book: Number the language of science Tobias Dantzig (in the reissue of 2005's classic 1930)
" Algebra is a scientific art. Its purpose are the numbers absolute and measurable quantities, which are unknown, but referring to anything known so that they can be determined, and this thing known is reached by analyzing the conditions of the problem in this art we look for relationships that link the magnitudes given the problem with the unknown, which, in the manner indicated above, is the subject of algebra. The perfection of this art consists in the knowledge of mathematical methods , with the help of which may be referred to the determination of both the numerical and geometric unknowns. Algebraic resolution, as is well known, is made only by an equation, that is, by matching some powers with others. "
This beautiful definition of algebra is the Persian poet Ghiyath al-Din Abu'l-Fath Omar ibn Ibrahim l-Nishaburi the -Khayyam (عمر بن إبرهيم خيام بيشابوري in Arabic), our poet of the last entry in his book entitled: "Treatise on Algebra problems demonstrations.
Omar Khayyam we will use the letter x for the unknown using the Arabic term for shay, meaning "thing", which was translated into English scientific works as x to y . In short, it was replaced by first letter, the initial x . Development
the first procedure of solving the quadratic and cubic equations from conic sections.
On this page, Omar is solving the problem: "a cube, the sides and the numbers are equal the squares ", or, in modern notation, x 3 + cx + d = bx 2.
The two conics whose intersection provides the solution is a circle and a hyperbola in the drawing, these curves intersect twice, thus providing two solutions of the cubic equation.
And since this post is old books:
virtual exhibition of ancient books, on the occasion of the year World of Mathematics, was held in Seville in December 2000 in the link:
THE CHILEAN GOVERNMENT VIOLATES HUMAN RIGHTS TO HOLD PRISONERS MAPUCHE SEVERAL MINOR . POLITICAL PRISONERS OF A NEW ETHNIC THREATEN HUNGER STRIKE AGAINST TERRORISM ACT OF PINOCHET
Minors Mapuche prisoners were interviewed in prison in Chol Chol. The interview, broadcast by the Association Mapuche Kilapan on Wednesday, November 24 was conducted by Julieta Vargas, a researcher at the Foundation for Support of Children Unprotected
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Luis, Cristian, Joseph, would like to know in his voice about the situation they face.
- Childbirth me. My name is Cristian Alexis Cayupan LofMuko Morales and I am from. I've been here more than 11 months awaiting trial preparation, which is suspended over and over again. I have my dad ill a few years ago with terminal cancer and I hate being away from él.Yo I think they have committed many injustices against us children, minors. For example, when I was arrested I was tortured, threatened me with my family saying they were going to do damage. I was beaten, tortured psychologically and physically.
Here time passes so sad, very sad is happening here. Despite everything we've done, writing, and a hunger strike, still here. For here we resisting as we can because most can not do: we're here, we already have them and have to fight just with our strength, our mind and ask the support people who read this. We want to tell him of the injustice done to the Mapuche children, with the Mapuche people, and we do not want the same thing happens to you my brother, my son, his grandchildren.
- What is happening today is, Cristian, for your community?
- In my community there is no longer young, are mothers, grandmothers, young children. Are those who are staying and continue to repress, still looking for more children to trick and show him to extract information threats.
- What sort of cheating children living in communities today?
- Children guys give away things, bring them toys, they bring cookies, cakes, and ask them things, they will visit a school and if they get caught on the street, interrogate and threaten.
-A nearly two months of the end of the hunger strike, what do you get it clear?
- I did not strike because my dad is sick and we have economic problems. But I find it unfair that we were to get young people to strike hungry to get some things, but hardly get anything. He had to risk the lives of adults and children.
-Luis, could you talk about yourself and explain your situation?
- Yes My name is Luis and I'm Marileo Manichaean community Guiñón Chief Joseph of the town of Ercilla. I already am going to serve seven months in this lugar.Yo see that injustice has been committed against us has been great because they have not respected our rights in any way.
We have removed from our schools, we have isolated our families, we have tortured, we are accused of terrorism, which are not, and we are prisoners here. Remember the Leonardo Quijón partner also came a day here, injured his leg and was about six months. He managed to prove his innocence at the trial, but no one took responsibility for the six months he was held prisoner, all the psychological damage caused and is causing us to us as well. The truth is that it is irreparable because they keep us prisoners when we know that no country has been accused of terrorist to a minor. Why us yes? I was a participant in the hunger strike. I spent 42 days without trying alimento.El government has told us that we took the Terrorism Act, but when we ask for relief, not give them because they did change the law has not been true, has not been complete. The government has misled the children and youth because we accused of being terrorists and we do not want to accuse us of libertad.A protected witnesses who say false things. They have no certainty that we have participated in the events. In fact, we are here because a witness, who nobody knows, happened to say that we were guilty.
I tell you we've never been involved in violence, we are estudiantes.Yo was in the middle third and worked at the Lyceum to study. Last year, I was not even a week and I went to look there, and I could not come back. Nobody cares about all the effort made by my mom, my family so I could study. The government does not respect our right to study and be with family, we have not been complied with anything.
"You who were on hunger strike, what things were achieved?
- My impression is that some things have changed, there are others that are the same as what he said Cristian about which we still apply the law to the menores.En my case, my dad asked for injunctive relief and even won two judges who voted in favor and a judge who voted against my freedom, the end was not because, as Terrorism Bill was, had to be the three in favor.
-José, can you tell us about yourself and why you are admitted to this hospital?
- I'm here because I am accused of being a terrorist for being Mapuche. I'm here to think differently, because my culture is different, because my thinking is different, because I am from a community that is in conflict, a place where the Chilean government has a conflict with communities because it does not return the land. Since I am a child, my community has been repressed by the state . I'm a prisoner here because there was no one else to stop in communities. For all adults are detained, they are now arresting children. We are holding Nose to us and then who will be caught. Since no one is exempt in the communities, only adult women, the elderly, they salvan.Nosotros months here and we have for long pause again for weary months because the change they made to the Act are not met, no We served it to us. They told us that we were not going to accuse more than terrorists, but we are still named as terrorists. We do not precautionary play, nothing, no rights we have accomplished.
I also did strike, thinking, thinking that at some point would solve everything. I lowered my hunger strike because my family was worried, also got in the government believe that at one point said that everything was solved. In the end it was all false, we were duped again, we were deceived by false words, they said that we had removed the Terrorism Act, but we like, we're still here and perhaps we'll be here much longer detention.
- What message would you give young Mapuche who are not, and they will read their words?
- My message is do not be alarmed do not be alarmed that the prison is not going to silence our people. This is a struggle and we must achieve it, do not be scared because we are young encarcelando.A ask them to support us from outside, to support us in one way or another, to all apoyen.Yo we want to convey this to the Youth: support us, we nevertheless continue what we are going strong. Maybe because today Mapuche torture us, haunt us, but certainly not going to give up. Hopefully those people who are sitting at home doing something for us, that children who are out does not happen as well as to nosotros.Yo I ask you to help us get our freedom and to help us that kids like us who do not same thing happen to his family does not suffer the same as our family is suffering. Help us not to re-commit these injustices, this torture, these delusions to children, such persecution not let them live as children: the rights that every child should have, (to be with his family, to study to achieve something of your life). I ask all those people help and support. Aguantaremos.Nosotros Here we do not want what happened to us happening to our brothers our children, or anyone in our blood, which is Mapuche .
resume the Mapuche hunger strike
The 17 indigenous Mapuche channeled under the Chilean Law antiterrotista, dating from the dictatorship of Augusto Pinochet , announced Tuesday that will reactivate the hunger strike to demand fair trials. The villagers await an official response to proceed with their peaceful protest.
According to spokesmen and family members of the community members at a hearing held this Tuesday, the Chilean Attorney faceless witnesses used by the video conferencing system and a voice-distorting mechanism, which caused the indignation of the accused.
The testimony against the Mapuche was considered by the defense as crude and thereupon the defendants, this protest, they withdrew to their cells.
considered view of the rigged trial, the detainees were determined to continue with the fast had been involved in until last October, over 80 days, whereby they asked the Chilean courts a fair trial.
The villagers believe that the Chilean government has given no response any of the three requests as being vital to the process to safeguard their rights. The Mapuche ask again that if judges are disqualified for having tried previously to one of the accused, the Prosecutor downgraded their crimes from being regarded as terrorists before trial, and finally that the Public Ministry not can use protected witnesses, as happened on Tuesday morning The Mapuche prosecuted expect official letter Minister Secretary General of the Presidency, Cristian Larroulet , which reflect the official position of the government of President Sebastián Piñera to the demands of the commoners. The letter is also the result of the mediation efforts between the Mapuche and the Chilean Executive by Archbishop Ricardo Ezzati , Archbishop of Concepción (city of southwest) .
Reiman Juana, mother of one of the Mapuche political prisoners, said the decision to take the villagers is imminent in view of which are still used to faceless witnesses in trials against the commoners, as occurred in recent days Cañete.
"The undercover witnesses remain. Negotiations with the Government wrong. Has not fulfilled all the promises and they want to resume the strike. They are not criminals or terrorists. They have families and are thrown away because they are convicted of crimes they have committed ", her mother said.
From Temucuicui community, the werken (messenger Mapuche) Jorge Huenchullán said the protests would resume only in Concepción, while in other prisons in the south will remain commoners alert, they do not see progress on the promise of the Executive. Huenchullán explains that in the case of re- condemnation of terrorist crime criminal offense "no commitments have materialized. Here the situation is that the brothers point calling for the reclassification of offenses. The Public Prosecutor has to change the charges, ie, should be prosecuted for common crimes and that has not materialized. "
From the Government as the Interior Minister Rodrigo Hinzpeter , expressed disagreement with the idea: "I hope no one resume the hunger strike. The truth is that everything that is committed is fulfilled and, therefore, feel that there is no reason. We must look to the future and we have been talking very well with indigenous peoples and I think we have very good news on the subject "he said.
Earlier, the Archbishop of Concepción , newly elected president of the Episcopal Conference, Ricardo Ezzati had warned that the Mapuche could take up the measure, which he intervened to put down the 34 villagers who remained in a prolonged hunger strike until October.
On that occasion, the Government undertook to remove the terrorism charges brought against the detainees. However, prosecutors refused to do so in the case of the attack on tax Elgueta. In addition, the Executive had announced the end of the covert use of witnesses and other measures taken within the framework of implementing the present Anti-Terrorism Act .
(Sources: Agrupación Mapuche Kilapan, teleSUR-Prensa Latina-The Third-Radio Bio-Bio and Radio Cooperativa)
A Story of Love and Astronomy: my contribution to the VIII Math Carnival
Mathematics lovers are in luck because we have a carnival in which to share our of interest. In this eighth edition in charge of this event is J uan Martínez-Giménez Tébar in his blog: Mathematicians are not serious people. It is my honor to participate in this opportunity with this entry:
We have said Oscar Wilde : The best way to get rid of temptation is to fall into it and yet we erre que erre rebelling; Luis Maria Anson brings the beauty of oriental poems in that love is constant before life.
mentions Anson Li Po , century Chinese poet XVIII, liberal and heavy drinker, just another one of my admired poets, Persian mathematician and astronomer Omar Khayyam (XI century), author of the Rubaiyaat and protagonist of the book Samarkand Amin Maalouf and film: The Keeper: The Legend of Omar Khayyam.
Drinking only in light of the moon
If Heaven had no love for wine, there would be no Wine Star in the sky. If the Earth had no love for wine, not have a city called Wine sources. As Heaven and Earth love wine, wine I can love without shame to Heaven. say that the clear wine is a saint, thick wine follow the path (Tao) of the wise. I have drunk deeply holy and wise, then what need to study the minds and the immortals? With three glasses penetrate the Great Tao, take everything a pitcher, and the world and I are one. Such things as I dreamed of wine, never be counted to the sober. (Li Po)
As what you ignore reserve tomorrow, try to be happy today. Grab a jug of wine, sit in the light of the moon and drink, as you say that perhaps tomorrow I will look in vain for the star of the night. (Omar Khayyam)
Similarities Eastern poets, passionate lives in coexisting stars and lovers, there is no time. Love and Astronomy. Anson referred to Tsing Kuan, XII century poet, rises to the stars love to sing the seventh night of the seventh moon. Tsiao Hsien Chiao is the love story of cowboy and Weaver, embodied in two stars that are every seventh night of every seventh moon. Then cross the celestial river, the Milky Way, on the bridge of the crows, and speak of love and sadness; the idea of \u200b\u200bconstant love, before life also appears dela in the Ching Dynasty, when you worship-yun chen, divine rhyme, Wa Lan, who loved his wife three million centuries before meeting ...
Poetry and Astronomy, Jayyamse Omar biography fascinates me all areas, as an astronomer to note that in 1070 he moved to Samarkand ( Samarkand, the most beautiful face that the Earth has ever gone into the sun.) where commissioned the construction of an astronomical observatory located in Marv (now Mary, Turkmenistan) was among a group of scientists who reformed the calendar Zaratustrano , the new schedule f ue formally inaugurated on March 15 1079, and is the calendar used by the Persians still . For this new caledario was called Yalalí calculated the length of a year with great accuracy. (An error of 1 day in 3770 years, less than the Gregorian calendar would begin to be used in Europe from October 15, 1582.)
The Persians had retained because Zaratustrano calendar accuracy, although the Islamic culture imposed on all nations conquered their lunar calendar.
Samarkand, city 2700 years old, declared by UNESCO as a World Heritage Site in 2001, one of the Sultans: Ulugh Beg had a great interest in astronomy and in 1428 built an astronomical observatory called inmneso Gurjani Zij.
cylindrical building had a height of 35 meters and a floor of 50 meters in diameter. Inside was a huge mural sextant Fajri marble 36 meter radio and a visual separation of 180 arc seconds, used for astronomical measurements for highly accurate for the year 1428.
In 1437 determines the length of the sidereal year as 365.2570370 ... d d = 365 h 6 m 10 s 8 (with an error s +58). In their actions used a gnomon of almost 50 meters high.
would have to spend 150 years until the calculations of Tycho Brahe Danish would improve the observatory in Samarkand.
The observatory was deliberately destroyed in 1449 but his remains were unearthed in 1908 and can be visited today as museum.
When we lack vocabulary all students and teachers say "that thing" ; effectively and referred to the unknown in the set of math problems and treaties Algebra as in the book of John the Baptist Tolra , published in Tarragona in 1619 : "Treaty of Art over Arithmetic, Algebra or call rule thing." 
the only solution is x = 1. 
Algebra is the offer made by the devil to the mathematician. The devil said, "I give you this powerful machine, who will answer any question. All you need is to give me your soul leaves the geometry and I will give this wonderful machine. (Michael Atiyah) 
