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Egyptians and nuragici, mathematics combines the two ancient populations

La Nuova Sardegna I read an interesting article online not signed on the study of a high school teacher who connects the Egyptian civilization nuragica and the terms of trigonometric. It seems to me a matter of great importance, even to be taken with the tongs. Here is the article:


CAGLIARI. An Italian scholar would find the thread that connects mathematics to that of the ancient Egyptian Sardi. In particular, the similarities between Egyptian and trigonometry nuragica show how one can speak of a common scientific civilization in the ancient Mediterranean.


The claims Nicolino De Pasquale, a professor of mathematics at the Volta School for Science and Technology of Pescara. The study of circular shields of the warriors Sardinians, decorated with drawings depicting the typical sine and cosine of the circles - said De Pasquale - to highlight the report, based on mathematical principles, with the ancient Egyptian game of snake, consisting in un disco inciso a scacchiera, che funge da sistema rappresentativo polare esponenziale.


Questa scoperta di Nicolino De Pasquale porta a concludere che fra i sudditi del faraone e i nuragici intercorre un rapporto speciale, basato tutto su metodi matematici condivisi e talmente innovativi da poter trovare ancora oggi applicazioni vantaggiose. De Pasquale, 61 anni, è un ingegnere aeronautico che vive e lavora a Pescara ed ha il pallino sulla matematica delle antiche civiltà. Ha risolto, ad esempio, l'enigma della matematica andina (nel 2000).


In seguito alla decifrazione dell'abaco Inca è stato, quindi, invitato a tenere conferenze in different foreign universities. Using the structure of an abacus Andean pre-Columbian civilizations of Huari and Tiwanaku precisely, he built a calculator for the blind, a touch operation (with pneumatic piston controlled by a PLC). He rebuilt the Egyptian musical scale, presented in Pescara in March 2006.


In January 2007, moreover, was published his work on pintaderas sardines, "Tempus Arrodas de '(Wheel of Time), deciphering the solar and lunar calendars nuragici. The pintaderas allowed to reconstruct, by analogy, the calendars used by the Egyptians, Greeks, and Celts, and to decipher the complex set of systems of solar and lunar Mediterranean basin in use in the first and second millennium BC

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slag slag Dragozilla

capitolo I

Nonostante il massacrante orario scolastico , le interrogazioni non programmate, le false promesse , Dragozilla , che I am and I do not need no introduction, still managed to follow the river of filth that is rampant in the country (unfortunately) real and that it undermines less common in places like ... Signorini's underpants, the pool or on the balcony of the BigBrother sora TettANGELO who really like to Iglesia's son (do not give the dear Gigi wants to redeem himself in doubt that giving it to a World's Aladdin Style).

The last months of my life have been difficult but full of love, from the correspondence of Patato & Potato where only a year ago there was an ugly and offensive written against the Minister: The fairy Enterogelmina. One who can do everything, even to leave unexplained intestinal blockage. Also fill empty adolescent afternoons .... So thank goodness there Patato!
So come on! Patati around the world, unite! Join
nell'ammmòre and screamed at the sky, both women know that you are ..
Because the school passes, the reforms pass, the ministers, the laws (as the Constitution has put down a camp in the waiting room), but no love! And then you watch to see how the tivvù amor vincit omnia. Just look at this new reality where you play the award several television programs from the masses ... .. that guy ... that transmit on all channels ... yes! Avetranakillers show! In Italy, several utilities are participating in several programs , Then this is also part of a good cause, I would volunteer to speak.
However the culprit of the crime of Sahara will eventually maybe a little life in prison (we think that the American version would be the death penalty!) .. But in the end with the love that reigns in this country, is the 'union, and the pain of a troubled mother who is referred directly to the death of her daughter so that everyone can suffer with her in front of the tivvù on while Sarkozy say "Oh Dieu!" simultaneously with the "Au DIENCA!" some poor gentleman in disguise. But after
... let us not forget that sooner or later arrives on Tuesday ... and then ... there XFucktor.
And by the way I wish someone would let me light the common thread running from Fuckinetti, passes from Tatta, comes all'Enrico arRUGGinERi, revolves around the language of 'whitewashed Shepherd (it will be a bit' of the wool of his sheep from ol'ispirazione Malgioglio bird?) enters between inlaccati Maionchi hair and God only knows if he comes out and goes to Elio. Tell me please! Tell me why you will Elio.
... It will be that all stories are those of the Jack human cases of participants in the game?
"Mystery" Henry the answer Arruggineri Calvo.

.. What then, let's face it, XFucktor is also not a bad program: listening to songs, they give advice , It comes to music. But our country would not be a bad country, but unfortunately the world is made up of people and People, radioactive waste and garbage disposal. So XF has become something very predictable, a pond that reflects the defects of this Bell'Italia: dubbed a public, judges, parliamentarians who enter into agreements under counter style Triumvirate, the Maionchi that the tenth minute shoot the first word, the phrases of Fuckinetti
and so on ... One of the many areas dominated by Captain Obvious and the patriotic rudeness.
But too much love in XF! What love! The homosexual couple, the club of juvenile hormones in an uproar, the circle of thirty cacciatrici.. Alla fine sono tutti amici, tutti lovers.
E chissenefrega se imbavagliano Santoro e se potresti trovare delle scorie giù per i fiumi dell’Appennino o potresti intravedere un termoSvalorizzatore sulle dolci alture reggiane..voglio dire.. c’è Patato!
Intanto noi non siamo come la Grecia , noi…….. non siamo come…………. no , non lo siamo…… o si ?

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Dragozilla

Chapter I

Despite the grueling school day, the questions have not been programmed, the false promises, Dragozilla who I am and I do not need no introduction, still managed to follow the river of filth that is rampant in the country (unfortunately) real and is danger in places that are less common as ... underpants Signorini, the pool of BigBrother or in the balcony of sora TettANGELO who really like to Iglesia's son (do not care like the dear Gigi in doubt redeem himself giving it a World at Aladin's Style).

The last months of my life have been difficult but full of love, from the correspondence of Patato & Potato where only a year ago there was an ugly and offensive written against the Minister: The fairy Enterogelmina. One who can do everything, even to leave unexplained intestinal blockage. Also fill empty adolescent afternoons .... So thank goodness there Patato!
So come on! Patati around the world, unite! Join
nell'ammmòre and screamed at the sky, both women know that you are ..
Because the school passes, the reforms pass, the ministers, the laws (as the Constitution has put down a camp in the waiting room), but no love! And then you watch to see how the tivvù amor vincit omnia. Just look at this new reality where you play the award several television programs from the masses ... .. that guy ... that that transmit on all channels ... yes! Avetranakillers show! In Italy, several utilities are participating in several programs, then this is also part of a good cause, I would volunteer to speak.
However the culprit of the crime of Sahara will eventually maybe a little life in prison (we think that the American version would be the death penalty!) .. But in the end with the love that reigns in this country, is the 'union, and the pain of a troubled mother who is referred directly to the death of her daughter so that everyone can suffer with her in front of the tivvù on while Sarkozy say "Oh Dieu!" simultaneously with the "Au DIENCA!" of some poor Knight masked. But after
... let us not forget that sooner or later arrives on Tuesday ... and then ... there XFucktor.
And by the way I wish someone would let me light the common thread running from Fuckinetti, passes from Tatta, comes all'Enrico arRUGGinERi, revolves around the language of 'whitewashed Shepherd (it will be a bit' of the wool of his sheep ol'ispirazione from bird Malgioglio?) enters between inlaccati Maionchi hair and God only knows if they go out and get to Elio. Tell me please! Tell me why you will Elio.
... It will be that all stories are those of the Jack human cases of participants in the game?
"Mystery" Henry the answer Arruggineri Calvo.

.. What then, let's face it, XFucktor is also not a bad program: listening to songs, you give opinions, talk about music. But our country would not be a bad country, but unfortunately the world is made up of people and People, radioactive waste and garbage disposal. So XF has become something very predictable, a pond that reflects the defects of this Bell'Italia: dubbed a public, judges, parliamentarians who enter into agreements under counter style Triumvirate, the Maionchi that the tenth minute shoot the first word, the phrases of Fuckinetti
and so on ... One of the many areas dominated by Captain Obvious and the patriotic rudeness. But
, quanto amore pure a XF ! Quanto amore! La coppia omo, il club degli ormoni minorenni in subbuglio, il circolo delle trentenni cacciatrici.. Alla fine sono tutti amici, tutti lovers.
E chissenefrega se imbavagliano Santoro e se potresti trovare delle scorie giù per i fiumi dell’Appennino o potresti intravedere un termoSvalorizzatore sulle dolci alture reggiane..voglio dire.. c’è Patato!
Intanto noi non siamo come la Grecia , noi…….. non siamo come…………. no , non lo siamo…… o si ?

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The Inn of Maria Stella

Eccovi miei cari buongustai, esperti nel gusto e nella scelta, dal palato fino e anche un po’ pignolo. Benvenuti nella mia cara e umile mensa, dove si servono piatti di prima qualità, dove il cambiamento è all’ordine del giorno, seppur inaspettato e sotto below, but there behind the counter, a little 'hated. Yet we have customers galore, some twist a little 'nose, others the precious but in the end always yield to temptation, others would not even come and sit a bit' on the sidelines.
What can I say, I'm more into the skin and let me illustrate my dishes prepared with as much patience and diligence. As a starter I would recommend a good "cut on the research" very good dish to start with a slap-up dinner, workhorse of our expert cook, perhaps to be enjoyed with a nice "Gelmot" dell'94, great little wine and mostatura still very archaic. No progress, no improvement, only secrets of long standing. Proceed
first chance with a nice, substantial aftertaste a bit 'edgy and electrifying "hours by 60 minutes" as you may get a slight start, given its duration, do not worry, the names of the dishes leave a little' make any difference as "Long Day Afternoon," but do not worry you will have to get used to a whole evening, which will seem long as a year or even years as, if not you will have some post-dinner tea.
The second course is simply a delicacy, but there are several drawbacks, if you have struggled to digest the first, I doubt you will succeed with what I'm about to explain, because it is a bomb, which goes straight to the stomach and immediately after invoked as a muse and kill the coffee coffee Well brace yourselves, we at the 'Osteria call it with great honor and enthusiasm "Train for Life" single dish created by our butcher Russo, following the tenets of "Made in Italy, flavored by an ounce of self-centeredness. If your liver is still screaming for help, then arranged a beautiful green glaze over with that plan, but that sun, that if my memory serves me must be so much in fashion these days even on carpet, especially on the benches on the windows in schools.
After a sigh, not of relief, on your belly triumphant, some will be pleased to call a waiter to have the bill so salty rather salty, but never for dinner so watch your wallet, if you were never with much money entered.
So let me give you impartial advice, do not arrive in this miserable condition is terribly embarrassing, always better to prevent any other business ... ... ... conseguenze, non trovate?
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The Mass is ended

Secondo il moderno senso comune, i giovani d’oggi sono una massa di soggetti indistinti, tristemente classificati in diverse categorie. Una vera e propria fiera degli stereotipi. Il problema si presenta quando, vittime di una tendenza passiva indotta dalla stessa società, la gente non mette in discussione quanto diffuso dalla diceria comune, considerandolo verità assoluta a cui nessuno si pone il problema di opporsi, soprattutto le vittime stesse. Spesso si esita nell'esprimere il proprio disappunto, nascondendosi dietro un silenzio ignorante e meschino.

Ma come può chi giudica in modo so superficial, accusing others of superficiality? How is it that all young people are so approved?

The simple answer is fear of exclusion, of being alone and helpless in front of that big bad monster called "Life." The solution, however, is to be able to say no to indifference and taboos of social credit.

The self-discovery becomes the protagonist in the life of every young person, the journey that will take into adulthood armed with projects and passions to cultivate.
growth is also about the search for the ideal dream of what can become a concrete, an ideal to follow: that there remain a dream forever.

There is no right time, the only way is to experiment.
must try, try their hand in many disciplines, finding inspiration, to interpret a model, change skin to be active.
Everything happened in the past, every man was born, everything happens for a change was because we said no, because one is opposed to something wrong, because you deleted
a stereotype.
there a place on the outskirts of Castelnuovo Monti, where diversity reigns. A multipurpose site victim, however, the famous killer Rating Given by common sense that hosts photographic exhibitions, debates, rehearsal room, cinema room, computer room and large play areas. Alternative.

experience is all well and good,
The Mass is ended,
go to the Youth Centre in peace.

"" If you sleep in the consciousness falls asleep, wakes up in the dream there. "
(M. Foucault)

Giulia Bedini

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No. 14 No. 14

To you, who think that the editors of Howl is a bit of faux highbrow 'snob.
to you, you would like to write about Howl but do not have the time and hide behind the phrase "No, I do not know much to write."
To you, who know perfectly well that is not true.
To you, that you're the 'skeptic teacher, the students enthusiastic. (Or the 'exact opposite, of course).
To you, who always ask "But when it comes out Howl?" And the editorial says, "But it's not something that you like writing?".
To you, that you use to make hats Howl painter. A
you who are convinced that this is not an editorial.
(You're absolutely right).
To you, you call Howl "Issue".
To you, who envy the chimneys because they are always smoking.
To you, that you use to make Howl paper toy airplane.
To you, that you wrote to Dr. G.
To you, who do you think Howl is an 'absolute waste of time. A
you who are tired of the usual routine home-school-bell-lessons-machines-mail.
To you, that you never lost a number of Howl.
to you, you've never picked up a number of Howl.
To you, that you forget easily.
To you, what are you afraid to forget.
to you, you did not know that Howl is a poem that was censored and deemed "obscene".
To you, who you know.
to you, think of I understood everything.
To you, that you realize you do not understand anything.
To you, that somehow you have contributed.
to you, you do too many problems.
To you, what do you do very little.
To you, that you're not even reading Howl. A

Allen Ginsberg, poet, writer, photographer, artist, man.


Benedetta Valdesalici

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Editorial Editorial

To you, who think that the editors of Howl is a bit of faux highbrow 'snob.
to you, you would like to write about Howl but do not have the time and hide behind the phrase "No, I do not know much to write."
To you, who know perfectly well that is not true.
To you, that you're the 'skeptic teacher, the students enthusiastic. (Or the 'exact opposite, of course).
To you, who always ask "But when it comes out Howl?" And the editorial says, "But it's not something that you like writing?".
To you, that you use to make hats Howl painter. A
you who are convinced that this is not an editorial.
(You're absolutely right).
to you, you call Howl "Issue".
To you, who envy the chimneys because they are always smoking.
To you, that you use to make Howl paper toy airplane.
To you, that you wrote to Dr. G.
To you, who do you think Howl is an 'absolute waste of time. A
you who are tired of the usual routine home-school-bell-lessons-machines-mail.
To you, that you never lost a number of Howl.
to you, you've never picked up a number of Howl.
To you, that you forget easily.
To you, what are you afraid to forget.
to you, you did not know that Howl is a poem that was censored and deemed "obscene".
To you, who you know.
To you, that you think you've understood everything.
To you, that you realize you do not understand anything.
To you, that somehow you have contributed.
to you, you do too many problems.
To you, what do you do very little.
To you, that you're not even reading Howl. A

Allen Ginsberg, poet, writer, photographer, artist, man.


Benedetta Valdesalici

Texas Culinary Academy

Humanism mathematician Piero della Francesca Piero della Francesca

figures and solids by Piero della Francesca


In classical antiquity, the role of symmetry as a guiding principle in the design of the physical world was accentuated by the rarity of solid figures symmetric similar to regular polygons.
while over the floor we have an infinite number of regular polygons corresponding to the finite rotations, three-dimensional space can be made only five polyhedra Regular: cube, tetrahedron, the 'octahedron, dodecahedron, el' Icosahedron. These regular polyhedra called Platonic Solids are traditionally the key role they play in cosmology developed by Plato. Him in his dialogues, Timaeus, associated with the tetrahedron, octahedron, cube, icosahedron, respectively, and those who were then considered the four basic elements: fire, air, land and water. The dodecahedron, not achievable by combining appropriate triangles (as
for the other polyhedra mentioned), however, was associated with the image of the entire cosmos, creating the so-called quintessence. This identification suggests an image of perfection that no doubt arises from the fact that the dodecahedron, approximates most of the other regular polyhedra the ball.
The fortunes of the Platonic solids scientific imagination of Western culture has been enormous, and is perhaps related to a philosophical point of view it believed it could penetrate deeply into the secrets of creation looking at these statues in the world of Euclidean Plato's ideas. Art and science blend in a deep way in the Libellus de corporibus regularibus of Piero della Francesca. The idea that inspires such a project is of a singular modernity in the sense that you want to support (we are in the late fifteenth century), the prejudices against the humanities, such as science or pure abstraction is not only technical but also a liberal art.

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5 4 Humanism mathematician Piero della Francesca Humanism mathematical

The mathematician and surveyor


The art of Piero della Francesca became one of the most conclusive expression of the first
renaissance generation. Are the direct ancestors Masaccio and Beato Angelico, he
express their achievements in perspective. The prospect gave a risposta all’esigenza, propria  delle culture umanistiche, di ricondurre l’esperienza del mondo alle norme chiare della ragione  umana. Nei dipinti nasceva il problema di rappresentare gli uomini e le cose su una superficie piana,  aggiungendo alle due dimensioni di altezza e di larghezza, quella illusoria della profondità. Proprio  con il "De Prospectiva Pingendi" la prospettiva avrà una formulazione più analitica e costantemente  fondata su basi geometriche euclidee, specialmente nel ‘400 fiorentino, per questo motivo Piero  della Francesca riceverà also the name of Euclid Renaissance.
With the prospect of the paintings of Piero della Francesca, the new criteria for representation of the real replace the static images of the thirteenth-century painting and look in the geometry of the forms and reports prospective relationship with things. The abstract and metaphysical of Piero della Francesca show that the outlook is not only necessary to those cultures which, tending to realism, entrust the task of reproducing the image of reality.
The artistic works of the painter of Sansepolcro Borgo show the tendency of man the fifteenth
to investigate and study the reality in which he lives, which leads him to define the laws of
perspective, to consider the images in their volume, their proportions.
In conclusion, we believe Piero della Francesca, as well as excellent painter, a mathematician of considerable validity, but the unique culture of mathematics was never in trouble artistic achievement since then use them as long as the was useful and was ready to leave when he was turn into a heavy presence.
The intent of Piero della Francesca, the greatest geometer of his time as Vasari says, is instead to compose, for the first time, following the example of Euclid's Elements, a treatise geometric size of an entire series of propositions, each with its own demonstration, logically linked together to form the true perspective as scientia. Piero is no doubt, more than any other the extraordinary blend of art and mathematics that if Leonardo spreads like a new thought on every piece of science, technology and art , Piero becomes aware in the subject of study, theoretical foundation of his story culture. Its three mathematical works, the Trattato d'abaco, De corporibus regolaribus and De prospectiva pingendi demonstrate a strong and original work on various aspects of mathematics Renaissance. The care in dealing with very complicated algebraic calculations, the centrality of theory of proportions, the taste for shapes and their multifaceted compose and decompose other forms, all filtered through the creative genius of the great painter contribute, we believe, to give to Western science, from which he takes up, the taste for beauty, for harmony that still persists in some scientists.
However, the attempt to Piero is still not c ompleta released from the medieval culture, with real errors in reasoning, with a often questionable logic, without a clear methodological framework of deductive characteristic of Hellenistic science and scientific thought in general.

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3

The mathematical treatises


Piero della Francesca is considered one of the greatest painters of our fifteenth century, but few students remember him as a man of science. The scientific papers of this famous painter, are three works of mathematics: "De corporibus regularibus", the "Trattato d'abaco" and "De prospectiva ping".
"De Prospectiva Ping" was the first real organic Treaty drawn up on the science of Renaissance perspective and so its validity is that for a long period of time would remain as an example and a source for later authors of works perspective. It was written around 1475, when its author was about sixty years old and had already given many proofs of his exceptional artistic talent. Divided into three books, this treaty clearly develops in a perspective representation of mathematical problems by providing practical examples not only related to complex geometric and architectural forms, but in any natural form. The first book, plane geometry, educational purposes has proved to be clear and precise drawings. The second, solid geometry,

perspective focuses on the representation of solids. The third book objectively determine the prospective image of complex objects.
In the two other minor writings, "De corporibus regularibus' and the 'abacus', the painter depth analysis of the bodies regular and almost regular.


PS: Picture taken from http://descrittiva4.blogspot.com/

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Humanism mathematician Piero della Francesca Piero della Francesca 2

The period and the ideas of artists contemporary



great things and great thoughts shook the minds of that small group of intellectuals, artists e scienziati, che nel '400 avrebbero riempito con i loro lavori i musei del mondo e dato la gioia nei secoli a venire di rivedere in quello una rinascita dell'Umanità. La riscoperta dei classici greci e latini riusciva a diffondere in quel gruppo la voglia di capire, di scoprire, di realizzare opere straordinarie. Queste potevano nascere solo all'interno di un pensiero scientifico e da una ricerca del bello e della misura, tutta umana come lo era quella di Euclide, Socrate o Fidia.
Sia Alberti, che Leonardo, che Piero della Francesca che per primi hanno scritto tesi sulla prospettiva, cercano una risposta nei metodi della geometria. Scriverà Leonardo:
... those who fall in love with practice without scientia are like sailors in ships that enter without a rudder or compass, who never sure where they go. Also the practice must be built upon the good theory, which is driving the prospect and leads and without this nothing is done well.
Piero della Francesca and perspective as to speak of true scientia. The rediscovery of classical culture, and especially the scientific one, obviously has a central role in this development.
Euclid and his Elements, variously translated and commented upon, will become a model of reference.

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Humanism mathematical

The life and works


The Life of Piero della Francesca seems soft edges and not completely uneventful memorable, almost entirely devoted to the craft of painting. We know that Piero was born in the town of Borgo San Sepulchre from a family of craftsmen and merchants probably between 1415 and 1420. The milestone of his youth is his presence in Florence, perhaps even at an age less than twenty years. In the early 40s had to return to Borgo San Piero Sepulchre where in 1442 is documented as a city councilor. At this time his first and most important committee, that the "baptism of Christ." Also from this period are frescoes of the "altarpiece of Mercy" commissioned by the company of Mercy Borgo Sansepolcro. Posterity are painted the "Flagellation" and "Sacred conversation" where most flock to the characteristics of geometric vision Piero della Francesca . The painter died October 12, 1492, the day the discovery of America and the end of Middle Ages, a date that marks a turning point in history.


In the centuries following the harmonious coexistence and ; symbiosis of art, humanities and science, glory and pride of the Renaissance, came gradually less and it is logical to wonder why. Among the various causes the fall of the geocentric system followed by the spectacular success of the new astronomy and Newton's law, a succession of scientific revolutions that have generated suspicions not only in the ecclesiastical hierarchy but also those who felt excluded by the elected, but unfortunately for some scientists modesty was a virtue.

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Mouse in English means a mouse ... :)

The computer mouse is translated into several languages, 'souris' in French, 'raton' in English, 'maus' in German. In Italian, the mouse is left mouse. They did not know the Americans of IBM when they published an instruction manual.
"Balls of mice are now available as spare parts. If your mouse has difficult to operate properly, or does it in spurts, it is possible that it will need a ball replacement. Because of the delicate nature of the replacement process of the balls, it is recommended that it be performed by a qualified expert. Before proceeding, determine what kind of balls he needs your mouse. To do this, just examine its underside. Balls of American mice are usually larger and harder than those of mice overseas. The procedure for removal of a ball depends on the kind of rat. The protection of the balls of the mice from overseas can be simply blown away with a paperweight on the protection of American mice must first be exercised a clockwise or counterclockwise. Normally, the balls of mice are charged with static electricity, but it is better to treat them with caution, to avoid unplanned. Once you complete the replacement, the mouse can be used immediately. It is recommended to staff trained to carry constantly with them a couple of balls in reserve, so as to ensure maximum customer satisfaction. In the event that the scarce spare balls, you can send a request to the central distribution using the following code ... "

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numbers and succession: metamathematical reflections, historical and educational activities on a song Leopardi (4)

4. Looking to the historic teaching
explicit attention the operational concept, then, is the basis of some important attempts
formalization of arithmetic. Such an attitude is
constant in the history of mathematics, as stated by F. Arzarello, L. Bazzini and
G. Chiappini:
"The development of the concept of numbers you can see how the conduct of
a chain of transitions from the operational and structural conceptions. On the other hand
, even before the process of generating new numbers were regarded as objects
, mathematicians used them and combines them into operations (Arzarello,
Bazzini & Chiappini, 1994, p. 9).

Concludiamo osservando che l'annotazione storica secondo la quale molto
spesso l'aspetto operativo precede quello strutturale, assume una netta rilevanza
in numerose questioni di didattica della matematica (8).
A. Sfard, in una nota ricerca (1991), dopo avere sottolineato la sostanziale
astrazione che caratterizza la matematica (9), sottolinea la possibilità di
concepire (e di presentare) parallelamente i contenuti matematici in termini
strutturali (interpretandoli, dunque, come "oggetti") ed in termini operativi
(interpretation, therefore, as "processes")
"Being able to see a mathematical entity as an object
means being able to refer to it as a real thing, a static ... and manipulate
as a whole ... Interpret the notion as a process means considering
as potential rather than actual entities, which comes to light in the face of a sequence of
actions. So while the structural conception is static ... itananea
and overall the operation is dynamic, sequential and detailed
"(Sfard, 1991: 4).
The Sfard also extends this distinction to coding (and the author seems
here again ideally records Leopardi mentioned above):
'verbal encodings can not be captured' at a glance 'and must
be processed sequentially, so they seem more suited to present
calculation procedures. Thus, the internal representation is not iconic
relevant to operational thinking "(Sfard, 1991, p. 7, re:
Hadamard, 1949, p. 77).
Without claim to exhaust a subject very deep and sensitive, even
from epistemological point of view, we can therefore conclude that the introduction of operational
many fundamental concepts of mathematics (and,
these, the elements of arithmetic ) is a particularly important
and debated in a teaching environment.

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numbers and succession: metamathematical reflections, historical and educational activities on a song Leopardi (3)

3. The intuitionistic setting: numbers and counting


We therefore refer in this paragraph, setting
intuitionistic arithmetic (5) by RL Goodstein (1957). Use the following symbols:
counting operator N
a, b, ..., l, ... objects
a & b, a & b & c, ..., L, L & a, ... sets of objects
recursively define the act of counting (6):
N (l) = 1
N (L & l) = N (l) +1
Let S be the operator leads to the conclusion that the successor (denoted by Sx
ie the successor of x).
The usual addition operation:
(a, b) → a + b
è definita ricorsivamente da:
x+0 = x
x+Sy = S(x+y)
Ad esempio, per determinare 6+3 si procede nel modo seguente:
6+0 = 6
6+1 = 7
6+2 = (6+1)+1 = 7+1 = 8
6+3 = (6+2)+1 = 8+1 = 9
La moltiplicazione:
(a; b) → F1(a; b) = a·b
è definita ricorsivamente da:
F1(x; 0) = 0


F1(x; Sy) = x+F1(x; y)
È quindi possibile una definizione ricorsiva di altre operazioni. Per ogni n
naturale, n≥2, definiamo ricorsivamente le operazioni:
Fn(x; 0) = 1
Fn(x; Sy) = Fn–1[x; Fn(x; y)]
Ad esempio, per n = 2 si ottiene la definizione ricorsiva di F2(a; b) = ab
(operazione di esponenziazione) (7):
F2(x; 0) = 1
F2(x; Sy) = F1[x; F2(x; y)] = x·xy
Per n = 3 si ottiene la definizione ricorsiva di un'operazione non usuale, che
possiamo indicare mediante la posizione F3(a; b) = ba:
F3 (x, 0) = 1
F3 (x, Sy) = F2 [x, F2 (x, y)] = (yx) x
It eg
F3 (x 1) = 1x = x
F3 (x, 2) = 2x = x ^ x
F3 (x 1) = 3x = x ^ x ^ x

Track Lengthjohn Deere Snowmobiles

numbers and succession: metamathematical reflections, historical and educational track on a leopard ( 2)

2. A look at history:
set of Peano axioms
From a historical perspective, says N. Bourbaki:
"Before the nineteenth century, it seems there has been no attempt to define the addition
and multiplication of natural numbers if relying
direct intuition; Leibniz is the only one who, true to its principles, is
expressly noted that the "obvious truth" as 2 +2 = 4 are also likely
demonstration if we reflect on the definitions of numbers that will appear
, he did not consider it as a given the
commutativity of addition and multiplication. But no further than his reflections on
this regard, and in the mid-nineteenth century, no progress had yet been reached
"(Bourbaki, 1963).
With the work on the concept of number (1891), Giuseppe Peano (1858-1932),
rielaborando alcune idee introdotte da Wilhelm Richard Dedekind (1831-1916)
nello scritto Was sind und was sollen die Zahlen? (1888), propose un'introduzione
assiomatica dell'aritmetica basata su tre concetti primitivi (l'unità, che in
una seconda stesura fu sostituita con lo zero; il numero; il successivo) e su sei
assiomi (definitivamente enunciati nel 1898 in Aritmetica, la II parte del II vol.
del Formulaire de mathematiques: Peano, 1908, p. 27; Kennedy, 1983):

Assioma zero. I numeri formano una classe (2).
Assioma I. Lo zero è un numero.
Assioma II. Se a è un numero, il suo successivo a+ è un numero.
Assioma III. Se s è una classe contenente lo zero e, per ogni a, se a appartiene
a s, il successivo a+ appartiene a s,; allora ogni numero naturale è in s
("principio di induzione": si tratta in effetti di uno schema di assiomi: Chang &
Keisler, 1973) (3).
Assioma IV. Se a e b sono due numeri e se i loro successivi a+, b+ sono uguali,
allora a e b sono uguali.
Assioma V. Se a è a number, its following + is not zero.
The second Peano addition is based on the following two conditions, given in the original symbolism
(Peano, 1908, p. 29):
Addition I. If a is a number, a +0 = a.
Addition II. If a and b are two numbers, a + (b +) = (a + b) +.
is clear the close analogy that links the introduction of Goodstein
(presented in the previous paragraph) to this one. By implication, therefore, Peano
shows that if a, b are numbers, even a + b is a number (see: Peano,
1908; demonstrations sono riportate in: Carruccio, 1972).
La relazione introdotta da Peano è un'applicazione: a→a+ avente per dominio
l'insieme dei numeri naturali e per codominio l'insieme dei numeri naturali
non nulli, e che è una biiezione. Si può inoltre dimostrare che Peano introduce
nell'insieme dei numeri naturali un ordine stretto.

Possiamo dunque concludere che dall'impostazione peaniana, basata sull'applicazione
che ad ogni numero naturale associa il suo successivo, emerge il
ruolo essenziale del concetto di successione.

Cover Letter For Trainee Dental Nurse Examples

http://blog.blogosfere.it/mte/mt-tb.php?tb_id=232196

For 4 friends who read my "box of things" that have been reviewed as an example "what not to do a blogger."
As my reviewer is right I hope to make it known right ( and alleviate the pain), stating his conviction that I post: http://sciencebackstage.blogosfere.it/2010/07/le-buone-pratiche-del-blogging.html and adding SCIENCEBACKSTAGE ( http://sciencebackstage.blogosfere.it ) to the blog rool on the side.

Chevy Silverado 427 Ss For Sale

Luca Pacioli After 500 Years

And here's the press release:


On 21 October 2010, with the presentation of the Conference Proceedings of study 500 years after Pacioli (Sansepolcro, 22 and May 23, 2009 ) was Pacioli review of the achievements of the Project and were presented the results of two years of study and research, which involved students, teachers and students of secondary schools of the Tuscan and Umbrian Tiber Valley, with the cooperation of local authorities, and of individuals and companies operating in the Territory. The speakers were Professors James Banker, Argante Ciocci, Roberto Manescalchi, Enzo Mattesini, Pier Daniele Napolitani, Fausto Casi (Mostra A scuola di scienza e tecnica) e Giovanni Cangi (Quaderno Pacioli fra Arte e Geometria). Ha introdotto la Prof.ssa Paola Refice, Presidente della Fondazione Piero della Francesca. Ha condotto Matteo Martelli, Presidente del Centro Studi Mario Pancrazi.
Nella Sala Conferenze della Fondazione Piero della Francesca, in Viale Aggiunti a Sansepolcro, il folto pubblico ha partecipato alla ricostruzione della figura intellettuale di Luca Pacioli ed ha avuto modo di constatare la validità scientifica del volume degli Atti. Dagli interventi degli studiosi e dei docenti è emerso che il volume del Centro Studi non solo rappresenta un aggiornamento importante delle conoscenze biografiche del frate del Borgo, ma raccoglie gli studi most up to date on the works of Francis, on behalf of its recognition to the language of science in late fifteenth and early sixteenth century, and illuminates the relationship between Piero and Luca Luca between Leonardo and, in the context of the statement of the mathematical sciences, Pacioli places the protagonist of the great revolution of printing with movable type.
The book will be presented by the President of the Centre, November 10, 2010 in Leon in Spain, during the proceedings of the VII Encuentro Internacional AEC. For an audience of experts in accounting and business management, the development program will be shown the work of Pacioli promoted by local authorities, da Aboca Museum e dal Centro Studi “Mario Pancrazi”. Partendo dal Convegno del 1994 (Luca Pacioli e la Matematica del Rinascimento) sarà illustrata la bibliografia pacioliana fino al volume degli Atti. Un’attenzione particolare sarà rivolta alle pubblicazione delle Edizioni Aboca, dalla monografia pacioliana di Argante Ciocci (2009) all’edizione in facsimile di tre manoscritti del minorita di Sansepolcro: il De ludo scachorum (2007), il De viribus quantitatis (2009), il De divina proportione (manoscritto della Biblioteca Universitaria di Ginevra) del 2010.
Il Centro Studi “Mario Pancrazi” nei prossimi mesi pubblicherà il terzo quaderno della Serie R&D diretta da Francesca Giovagnoli, the result of the seminar devoted to astronomy January 31, 2010 (Conference Room of the Diocesan Museum of Città di Castello) and will contribute to the realization, in cooperation with the Central Apennines Business - Review of Territory and boarding INPDAP "Regina Elena", the seminar entitled economy after the crisis - Labor / Business / Company (Theatre Hall boarding INPDAP, 3 and 4 December 2010). They are in the works, finally, two initiatives: the Leonardo Project and the Tiber Valley, which includes a seminar and to publish the papers by the end of 2011 and an International Meeting on June 19 in Sansepolcro that will take stock on the biography and on pacioliana 'importance Brother of mathematics in the history of accounting and business economics.

Chlamydia In The Mouth

numbers and succession: metamathematical reflections, historical and educational activities on a song Leopardi (1)

GIORGIO TOMASO BATHROOMS


1. Medley of thoughts, November 28, 1820
wrote the twenty-two Giacomo Leopardi:
"The man without the knowledge of a speech, can not conceive the idea of \u200b\u200ba fixed number
. Imagine you have thirty or forty stones,
senz'avere a name to be given to each one, that is, one, two, three,
to the last name, ie thirty or forty, which contiene la
somma di tutte le pietre, e desta un'idea che può essere abbracciata tutta in uno
stesso tempo dall'intelletto e dalla memoria, essendo complessiva ma definita
ed intera. Voi nel detto caso, non mi saprete dire, né concepirete in nessun
modo fra voi stesso la quantità precisa delle dette pietre; perché quando siete
arrivato all'ultima, per sapere e concepire detta quantità, bisogna che l'intelletto
concepisca, e la memoria abbia presenti in uno stesso momento tutti
gl'individui di essa quantità, la qual cosa è impossibile all'uomo. Neanche
it should help the eye, wanting to know why the number of certain objects
present, and not knowing how to count, you need the same operation and simultaneous
individual memory. So if you do not know except one
numerical designation, and counting could not say more than one, one, one;
to how much attention you would put, akin to collect progressively
with the soul and memory The precise amount of these units until the last, you'd
in the same case. So if I did not know that two other names
etc.. Except a very small amount, like five or six, which
memory and intellect can not conceive of speech, because you get to
simultaneously present all it amounts to a few individuals ... Typically
the idea of \u200b\u200bthe precise number, or with the help of speech or not, has never
instantaneous, but composed of succession, more or less long, more or less
difficult, according to the measure the amount (by Zibaldone of thoughts, 28 November 1820
: Leopardi, 1969).
This track offers some reflections on the concept of natural number.

First, it is clear the central importance that the author attributes to the language
(1). Early onset ("The man without the knowledge of a speech,
can not conceive the idea of \u200b\u200ba fixed number), in fact, Leopardi
explicitly refers to the essential role of the name of the individual numbers
natural: it is thanks to 'name' that we can enumerate the elements of a finite
(that we can identify, gradually, his
subsets of increasing cardinality) until you hear the whole
(to fix "an idea that can all be embraced in the same time
intellect and memory, but defined as total and complete ").
This concept is therefore closely linked to the numerical count, when
to enumerate: the role of the 'speech' is to be decisive in its
as it allows the unfolding of the proper implementation of such a measure ("And so if you do not
I knew except a single numerical designation, and counting
could not say no more than one, one, one ...»). Leopardi, towards the end of the passage quoted,
clearly recognizes that the very concept of numbers through (and beyond)
the succession of 'Name', is linked inextricably
to count ("The idea of \u200b\u200bthe exact number, or with the help of speech or not, is not
never instantaneous, but composed of succession) (Borg & Pepe, 1998).
This consideration can be modern and thorough recovery
by examining some of the settings of arithmetic, as we shall see that based on the introduction of recursive
their roots.

Tackfilm.se After Effects

The Abraham Lincoln connection

From site http://www.mathopenref.com/euclid.html

At age forty, Abraham Lincoln Studied Euclid for training in reasoning, and as a traveling lawyer on horseback, kept a copy of Euclid's Elements in his saddlebag. In his biography of Lincoln, his  law partner Billy Herndon tells how late at night Lincoln would lie on the floor studying Euclid's geometry by lamplight. Lincoln's logical speeches and some of his phrases such as "dedicated to the  proposition" in the Gettysburg address are attributed to his reading of Euclid.

Lincoln explains why he was motivated to read Euclid: "In the course of my law reading I constantly came upon the word "demonstrate". I thought at first that I understood its meaning, but  soon became satisfied that I did not. I said to myself, What do I do when I demonstrate more than when I reason or prove? How does demonstration differ from any other proof?

I consulted Webster's Dictionary. They told of 'certain proof,' 'proof  beyond the possibility of doubt'; but I could form no idea of what sort of proof that was. I thought a great many things were proved beyond the possibility of doubt, without recourse to any such extraordinary process of reasoning as I understood demonstration to be. I consulted all the dictionaries and books of reference I could find, but with no better results. You might as well have defined blue to a blind man.

At last I said,- Lincoln, you never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father's house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what demonstrate means, and went back to my law studies."

Silvercitymovie Theatre Kitchener

Untitled

than the cry of the flesh

no key
us shut up;


escape in the first
darkness.

Anna Palaces

Howl No. 11

Contracting Herpes From A Razor

absurd

In a country of the Apennines, two brothers bought a small pig, they have put in a little hole, where there was a hole from a small pig was able to get out, but came to 2 pounds, when it came time to slaughter, never went out of the hole, then had to work to destroy the walls.

Such recounts his trip to Switzerland, the train has left that there was snow, the tunnel was so long that when he arrived there were already ripe cherries.

It is said that a mole digging in the ground, he dropped the light poles and telephone, the villagers of the place, after so many emplacements, have captured and to punish her, they buried alive.

A that was in a French park, was caught near a small lake with ducks, the park is near a guard and tells him "you are stealing the ducks," and he replied: "No I'm teaching him to swim."

It is said that in a mountain village, there were some cold days, a man returning from a tavern, after drinking a few glasses more on the way back, he lost so hard to pee, you had to stop to do it , pee froze just before going to the ground, which had formed an arch of ice.

Always there and always the cold had frozen all the chickens, the people, they had to bring them near the stove, then it was snowing così tanto che le galline “portavano gli stivali e beccavano le stelle”.


Sebastiano Beretti

Median Bmi Females Canada

the Apennines near

La nostra scuola ci offre, anno dopo anno, una grande quantità di iniziative, progetti, possibilità di crescita e di nuove conoscenze.
Sta poi a noi, studenti, farci conoscere, spendere tempo ed energie, in ottica futura, per cercare di accendere una lampadina sulla nostra strada.
Allora ecco che molte azioni che compiamo le cominciamo per curiosità, quasi per caso e questo si rivela poi alla fine qualcosa di veramente interessante.
Ed è così che un anno fa, noi gruppo delle ormai ex-quarte, tra liceo , ITI, geometri, abbiamo deciso di aprire a window on the world and our future. Thanks to the group EFPE and mountain community, we realized the importance of all that is marketing and communications, promoters of objects and people, also studying every little publicity. We started
strategies global giants, up to the study of our mountains, our history and our mentality.
Many times we escape from all that we are, we try something outside their normal hits us.
only fair.
Unfortunately, many times, we realize that everything we need is right next to us, you are not convinced?

The Apennines close ... on youtube!


Children Project

Howl No. 11

How To Repair Hd Cable

Women

The word comes from our beloved Latin woman "Domna", syncopated form of "dominating" or "mistress." The use of this term came to life in Tuscany in the thirteenth century, and then spread throughout Italy. Before it was in fact used the word "female". This figure has always been rather discriminated against in many cultures and historical backgrounds prior to today, where the woman was recognized only the ability to procreate and to care for children, family and home. Even today there are cultures where the woman has una condizione simile di considerazione e, per questo, subisce maltrattamenti ed onte. Prendiamo come esempio uno dei più discussi e rilevanti: la condizione della donna nell’Islam. La complessa relazione tra la donna e l’islam viene trattata sia dai testi islamici, sia dalla storia e dalla cultura del mondo islamico. Il testo religioso principale, il Corano, ci rivela l’uguaglianza tra uomo e donna di fronte al proprio Dio ma a legge islamica, la Sharia, comprende, invece, distinzioni tra i ruoli di genere, i diritti e i doveri dei due sessi. Abbiamo perciò, tra gli interpreti delle norme giuridiche, differenti correnti di pensiero che si distinguono tra i più conservatori, i quali sostengono che le diversità tra uomo e donna siano dovute a differenti status e responsabilità e tra il liberalismo musulmano, il femminismo islamico ed altri gruppi che hanno esposto argomentazioni ed interpretazioni più aperte ed innovative rispetto al pensiero tradizionale. Va detto che nei paesi a maggioranza musulmana vengono concessi alla donna vari diritti per quanto riguarda il matrimonio, il divorzio, i diritti civili, lo status legale, l’abbigliamento e l’istruzione basandosi sulle diverse interpretazioni della dottrina islamica e sui principi di laicità. Tale situazione è notevole in quanto come Capi di stato di questi territori ci sono delle donne. Sicuramente questo è un importante traguardo raggiunto dalle donne islamiche, ottenuto grazie al lavoro e al sacrificio associations and movements to defend them. However there is no need to speak in terms too general on the conquest of these rights, as it is required more careful analysis of individual Islamic countries once again distinguished between the more traditional, where women are considered inferior, and those with a more fair.
not only the Muslim woman, however, in the course of history has managed to achieve certain rights, but rather the entire world of women. Through numerous socio-historical battles we see today at the head of a State, a Minister or even a woman of a major company. We follow, then, some milestones of this statement through historical facts. The women's suffrage

-1945: the Italian teens can vote on the Senate needed 25 years.
In many countries, including some of those who today are considered "inferior" to the women it was already the law: Albania, Armenia, Australia, Austria, Azerbaijan, Belgium, Bolivia, Brazil, Burma, Canada, Philippines, Finland, Ireland , Iceland.

Giulia Bedini Howl No. 11