61. MATEMÁTICOS Y MATEMÁTICAS EN EL MUNDO GRIEGO Translate this page A raíz de la polémica entre Cardano y Tartaglia, rafael bombelli, el último delos algebristas italianos del Renacimiento quien había leido el Ars Magna de http://euler.us.es/~libros/aritmetica.html

De Euclides a Newton: Los genios a traves de sus libros principal griegos iberia De consolatione philosophiae Opera n(n+1)/2 3n(n-1)/2 rithmetica integra rithmetica integra Practica Arithmeticae Ars Magna x Ars Magna -debemos destacar que el Ars Magna de Cardano estaba escrito de manera muy poco clara-. Su obra L'Algebra L'Algebra idea loca Canonem mathematicum principal griegos iberia Renato Alvarez Nodarse ... ran @us.es

62. Biography-center - Letter B Bombardier, Joseph schwinger.harvard.edu/~terning/bios/Beaverbrook.html; bombelli,rafael wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/bombelli.html; http://www.biography-center.com/b.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish B 1122 biographies Baade, Walter www.treasure-troves.com/bios/Baade.html Baade, Wilhelm Heinrich Walter www.phys-astro.sonoma.edu/BruceMedalists/Baade/index.html Baastrup, Christian Ingerslev www.whonamedit.com/doctor.cfm/1242.html Babashoff, Shirley www.hickoksports.com/biograph/babashof.shtml Babbage, Charles www.norfacad.pvt.k12.va.us/project/babbage/babbage.htm Babbage, Charles www.ideafinder.com/history/inventors/babbage.htm Babbitt, Bruce www.doi.gov/bab_bio.html Babbitt, Platt D. www.getty.edu/art/collections/bio/a2841-1.html Babcock, George www.invent.org/hall_of_fame/6.html Babcock, Harold Delos www.phys-astro.sonoma.edu/BruceMedalists/BabcockHD/index.html Babcock, Horace Welcome www.phys-astro.sonoma.edu/BruceMedalists/BabcockHW/index.html Babcock, Stephen Moulton

63. Algebra In The Renaissance, Part 2 I found this part of the lecture particularly interesting and thought he did a goodjob presenting it. The next mathematician discussed was rafael bombelli. http://public.csusm.edu/public/DJBarskyWebs/330CollageOct17.html

Algebra in the Renaissance, Part 2 The discussion was started by talking about art in the Renaissance. The idea of perspective in a painting began to be used in the Renaissance. To achieve realism, objects further away must be made to appear smaller. The painter Leon Battista Alberti (1404-1472) wrote a text on the subject of geometry as it relates to perspective in painting. The main topic centered around solving the "cubic" problem. Several mathematicians of the fifteenth and sixteenth century built upon the work of the Islamic mathematicians. We discussed Scipione del Ferro (1465-1526) who discovered an algebraic method for solving the cubic equation x ^3 + cx = d. Del Ferro taught Antonio Fiore. Niccolo Tartaglia (1499-1557) claimed that he discovered the solution to the cubic equations of the form x^3 + bx^2 = d. Tartaglia told Gerolamo Cardano his secret, however Cardano published the work when he discovered that it had earlier been discovered by del Ferro. It is interesting to follow the long history of one problem. After Dr. Barsky's commentary on the lack of a Nobel prize for mathematics and the mathematician of the day (Vickery), David Trigg began to talk about how the third dimension was represented in the art of this time period. The topics covered consisted of Copernicus and Kepler in Astronomy, the addition of perspective to make two dimensional art appear as three dimensional, Scipione Del Ferro, Antonio Fiore, Niccolo Tartaglia, Gerolamo Cardano and the "Artis Magnae", Libre de Ludo Aleae, Raphael Bombelli, and Simon Stevin.

64. A Look To The Past In 1572 rafael bombelli (15261573) published his treatise, Algebra, in which hegave one more step in the solution of cubic equations, expressing solutions in http://ued.uniandes.edu.co/servidor/em/recinf/tg18/Vizmanos/Vizmanos-2.html

65. LE EQUAZIONI DI TERZO GRADO Translate this page Questo problema stimolò, negli anni successivi, numerose ricerche in campo algebricoche portarono con rafael bombelli all’introduzione dei numeri immaginari http://www.mbservice.it/scuola/tartaglia/le_equazioni_di_terzo_grado.htm

LE EQUAZIONI DI TERZO GRADO La risoluzione delle equazioni di terzo grado aveva appassionato i matematici di tutti i tempi, poichè era frequente imbattersi in problemi di grado superiore al secondo. Per quanto riguarda la soluzione algebrica delle equazioni cubiche, visti gli insuccessi, gli algebristi concludevano che il caso era impossibile oppure procedevano per tentativi. che gli era stata proposta da un astronomo di Federico II. Fibonacci pervenne al sorprendente valore approssimato x =1,3688081. Nel 1500 cominciarono a circolare voci sui progressi della matematica in campo algebrico, tanto è vero che nel 1530 Zuanne de Tonini da Coi inviò a Tartaglia due problemi che si risolvevano con equazioni di 3° grado. Assai polemica fu la lettera di Tartaglia in risposta a Zuanne, riportata nel Quesito XIII : "… et dico che vi dovreste alquanto arossire, a proponere da rissolvere ad altri, quello che voi medesimo non sapeti rissolvere…". ".. conducevano l’operatore in el capitolo de cosa e cubo equal a numero…" Tartaglia mise la sua invenzione in versi , non sempre molto chiari, per paura che altri potessero pubblicare la sua scoperta.

66. Matematik rafael bombelli var interesseret i at fuldstændiggøre kvadratrødderne, ogvar dermed med til at finde det vi i dag kalder for de komplekse tal. http://fp.worldonline.dk/fpeneven/matematik.htm

På disse sider vil forskellige betydningsfulde og måske for os ukendte matematiske genier få deres berettigelse. Siderne vil løbende blive opgraderet, og det er min hensigt at udvide siderne til at indeholde betydningsfulde fysikere. Ved at klikke på billederne eller linksene herunder, kan du læse mere om de enkelte personer. Casper Wessel Norsk født landmåler, der var den første med en geometrisk indførsel af de komplekse tal. Desværre var den nærmest ukendt, da den kun udkom på dansk! Rafael Bombelli var interesseret i at fuldstændiggøre kvadratrødderne, og var dermed med til at finde det vi i dag kalder for de komplekse tal. Disse sider er sidst opdateret d. 8/6-2000 Leonardo Fibonacci af Pisa Italien i 1300-tallet, fandt nogle malere ud af, at man matematisk kunne beregne, hvordan en figurkomposition skulle bygges op for at tage sig bedst og mest harmonisk ud nemlig via "Det Gyldne Snit". John Napier ( var godsejer, han havde ikke nogen videnskabelig stilling, men var altid optaget af forsk ning i matematik eller andre videnskaber.

67. Untitled Translate this page Le notizie sulla vita di rafael bombelli provengono tutte da un'unica fonte lasua OPERA sull'ALGEBRA, pubblicata nel 1572 e conservata manoscritta nella http://www.itaer.it/lavori/complex/storia.htm

Storicamente il problema di algebra che condusse ad un ampliamento del campo dei numeri reali è stato quello di cercare una formula risolutiva per le equazioni di terzo grado. In tale ricerca S. DAL FERRO (1465-1526), introdusse alcuni simboli che trattava alla stessa stregua dei numeri reali e che più tardi vennero chiamati numeri complessi. Una trattazione autonoma di questi nuovi enti si ebbe soltanto cinquant'anni più tardi ad opera del grande algebrista R. BOMBELLI (sec. XVI). Le notizie sulla vita di Rafael Bombelli provengono tutte da un'unica fonte: la sua OPERA sull'ALGEBRA, pubblicata nel 1572 e conservata manoscritta nella Biblioteca dell'Archiginnasio di Bologna. I numeri complessi entrarono però definitivamente nell'Analisi Matematica ai primi del secolo XIX dopo che WESSEL e ARGAND ne ebbero data una rappresentazione geometrica. C.F. GAUSS (1777-1855) contribuì alla sistemazione della teoria dei numeri complessi ed alla loro diffusione in Europa. Torna alla pagina iniziale

68. Week99 eg 4) Luca bombelli, Joohan Lee, David Meyer and rafael D. Sorkin,Spacetime as a causal set, Phys. Rev. Lett. 59 (1987), 521. http://math.ucr.edu/home/baez/week99.html

March 15, 1997 This Week's Finds in Mathematical Physics (Week 99) John Baez Life here at the Center for Gravitational Physics and Geometry is tremendously exciting. In two weeks I have to return to U. C. Riverside and my mundane life as a teacher of calculus, but right now I'm still living it up. I'm working with Ashtekar, Corichi, and Krasnov on computing the entropy of black holes using the loop representation of quantum gravity, and also I'm talking to lots of people about an interesting 4-dimensional formulation of the loop representation in terms of "spin foams" - roughly speaking, soap-bubble-like structures with faces labelled by spins. Here are some papers I've come across while here: 1) Lee Smolin, The future of spin networks, in The Geometric Universe: Science, Geometry, and the Work of Roger Penrose, eds. S. Hugget, Paul Tod, and L.J. Mason, Oxford University Press, 1998. Also available as gr-qc/9702030 I've spoken a lot about spin networks here on This Week's Finds. They were first invented by Penrose as a radical alternative to the usual way of thinking of space as a smooth manifold. For him, they were purely discrete, purely combinatorial structures: graphs with edges labelled by "spins" j = 0, 1/2, 1, 3/2, etc., and with three edges meeting at each vertex. He showed how when these spin networks become sufficiently large and complicated, they begin in certain ways to mimic ordinary 3-dimensional Euclidean space. Interestingly, he never got around to publishing his original paper on the subject, so it remains available only if you know someone who knows someone who has it:

69. DIARI AVUI - Suplement Cultura Richard Hamilton, Marcel Duchamp, Frank Stella, Xavier Corberó, rafael Canogar,Eduard ArranzBravo i el citat John Cage, de qui el 1982 bombelli va finançar http://www.avui.es/avui/diari/02/jul/25/k40125.htm

UN RECORREGUT ARTÍSTIC, GEOGRÀFIC I HISTÒRIC Pobles que sedueixen els creadors JORDI MARLET electrik@eresmas.net La llum i la silueta del paisatge, la tranquil·litat del lloc o la bohèmia han fet de Sitges, Tossa de Mar, Ceret i Cadaqués pobles preferits dels creadors. Avui en dia, Sant Esteve de Palautordera, Vespella de Gaià i Arsèguel s'afegeixen a la llista de pobles catalans amb tradició artística J a des de la dècada dels vuitanta del segle XVIII i per una sèrie de circumstàncies, Sitges (Garraf) va aglutinar artistes de la tendència luminista amb què després ha estat associada la vila. Hi vivia Joan Roig Soler. Arcadi Mas i Soldevila, que és el pintor dels pobles blancs per excel·lència, s'hi havia instal·lat aleshores, a causa del seu matrimoni amb una sitgetana. També Eliseu Meifrén -que era el menys sitgetà de tots però el de més empenta- va passar per Sitges. Venia de París, on Casas, Rusiñol i Utrillo vivien el seu millor moment al cim del Montmartre. L'octubre del 1891, ell i Rusiñol, que anaven en tartana a Vilanova i la Geltrú, hi van parar. Així es va iniciar el contacte dels artistes modernistes amb Sitges. Rusiñol es va acabar instal·lant al Cau Ferrat, centre de les festes modernistes. "La mateixa ubicació [del Modernisme] a Sitges ja era en ella mateixa una fugida de la realitat que es vivia a Barcelona", indiquen Francesc Miralles i Ferran Fontbona al volum setè de la

70. Cardano Y Tartaglia Translate this page Mucho más que un triángulo Gerolamo Cardano. Renacentista tenazLudovico de Ferrari. La idea en un destello rafael bombelli. El http://www.nivola.com/cardanoindex.htm

De la Edad Media al Renacimiento El siglo XV Las matemáticas del ábaco Regiomontano y la trigonometría Alberto Durero y la geometría El calendario gregoriano. Un problema de astronomía Luca Pacioli y la Summa de Arithmetica Dos problemas de Maestro Biaggio comentados por Maestro Benedetto Los versos con los que Tartaglia comunicó la solución a Cardano La demostración de Cardano de la regla de la ecuación cúbica Análisis de la demostración de Cardano La resolución de la ecuación general de tercer grado La demostración de Bombelli El caso irreducible y los números complejos La resolución de la ecuación de cuarto grado Los protagonistas de esta historia Scipione del Ferro. El álgebra en silencio Niccoló Tartaglia. Mucho más que un triángulo Gerolamo Cardano. Renacentista tenaz Ludovico de Ferrari. La idea en un destello Rafael Bombelli. El valor de la claridad Puntos suspensivos Panorama de los siglos XV y XVI Bibliografía Portada Contraportada Otras obras

71. Pronunciation Guide For Mathematics János Bólyai 180260 'bahl yah ee. rafael bombelli 1526-72. NapoleonBonaparte 'boh nuh part. George Boole 1815-64 bool. Boolean 'boo lee uhn. http://waukesha.uwc.edu/mat/kkromare/up.html

Mathematics Pronunciation Guide A Megametamathematical Guide for Proper American English Pronunciation of Terms and Names, for the Diacritally Challenged This guide includes most mathematicians and mathematical terms that may been encountered in high school and the first two years of college. Proper names are generally pronounced as in the original language. Some entries are obscure and may be useful only in a game of mathematical trivia, e. g. d'Alembert's mother, the name of the line in a fraction, or who shot Galois. I have not had the time to include most definitions or accomplishments. The curious person may try searching the internet for such information. However I have given a few, they are indicated with Move the curser to the symbol and wait a second. D ates include B.C. or A.D. only if the choice is not obvious from the context. The Guide is not complete, I will be adding more pronunciations and entries as time permits. (I did not give up my day job.) (The red dates and purple pronunciations are not links.)

72. Untitled Document Translate this page rafael bombelli, trinta anos depois, volta à dúvida de Cardano ea discute emtermos de raízes de equações, para as quais criou uma notação própria. http://www.prandiano.com.br/html/m_livro.htm

ARQUEOLOGIA MATEMÁTICA A origem da Matemática nas civilizações antigas Arqueologia Matemática As origens da Matemática nas civilizações antigas é um livro que mostra e discute a arte de calcular na antigüidade e, o mais importante, como os antigos a aplicavam e em que áreas do conhecimento humano. ASSIM NASCEU O IMAGINÁRIO Origens dos Números Complexos Raiz quadrada de um número negativo? Cardano não poderia imaginar em 1542 o avanço matemático que sua dúvida produziria, pois seus colegas de ofício argumentaram ser pura ingenuidade questionar ( ). Sufocado pelas críticas e problemas familiares - um de seus filhos foi enforcado -, Cardano abandona a Matemática e passa a dedicar-se à Medicina. Rafael Bombelli, trinta anos depois, volta à dúvida de Cardano e a discute em termos de raízes de equações, para as quais criou uma notação própria. Apesar desse estudo de Bombelli não ter elucidado o conceito de raiz quadrada de um número negativo, influenciaria, e muito, René Descartes, que, em 1637, convocaria os filósofos europeus para desenvolverem tal assunto que chamou de Étude Imaginaire (Estudo Imaginário). Leibniz não concordou com esse nome por achá-lo inexpressivo, e em 1702 propôs

73. List Of Mathematicians For The Biography Report Bernoulli, Johann 11. Bolzano, Bernhardt 12. bombelli, rafael 13. Briggs, Henry14. Cantor, Georg 15. Carroll, Louis 16. Cauchy, AugistinLouis 17. http://www.cabrillo.cc.ca.us/~mladdon/m15mathematicians.html

Mathematicians for the Biography Poster project 1. Abel, Niels Henrik 2. Agnesi, Maria 3. Al-Khwarizmi, Muhammad 4. Archimedes 5. Asimov, Isaac 6. Babbage, Charles 7. Berkeley, George 8. Bernoulli, Daniel 9. Bernoulli, Jacob 10. Bernoulli, Johann 11. Bolzano, Bernhardt 12. Bombelli, Rafael 13. Briggs, Henry 14. Cantor, Georg 15. Carroll, Louis 16. Cauchy, Augistin-Louis 17. De Laplace, Pierre-Simon 18. De Pisa, Leonardo 19. DeMoivre, Abraham 20. Descartes, Rene 21. Du Chatelet, Emilie 22. Durer, Albrecht 23. Dyson, Freeman (Physics) 24. Einstein, Albert 25. Erdos, Paul 26. Euclid 27. Euler, Leonard 28. Fermat, Pierre 29. Gauss, Carl 30. Germain, Sophie 31. Godel, Kurt 32. Hilbert, David 33. Hopper, Grace 34. Hypatia 35. Keynes, John M. (Econ) 36. Khayyam, Omar 37. Kovalevskaya, Sofia 38. L’Hopital, Guillaume 39. Lagrange, Joseph-Louis 40. Leibnitz, Gottfried 41. Lovelace, Ada Byron 42. Maclaurin, Colin 43. Malthus, T. R. (Biol) 44. Napier, John 45. Nash, John 46. Newton, Isaac 47. Noether, Emmy 48. Oresme, Nicole 49. Polya, George 50. Ramanujan, Srinivara 51. Riemann, Georg F.

74. Lit-Bio-Graph Translate this page München (Karl M. Lipp Verlag), S. 516. bombelli, rafael (1526-1572), Wasserbauingenieur(I), DSB 2 (1975), S. 279-281. Boos, Carl (1806-1883), nass. http://www.wasserarchiv.de/Lit-Bio-Graph.htm

Biographische Nachweise ADB = Allgemeine Deutsche Biographie NDB = Neue Deutsche Biographie Aconio - Arnd Aconcio , Jacopo (1500-1566), Theologe u. Ingenieur (I) In: Dictionary of National Biography, Bd. 1 (1972), S. 63-65. London. Adams , Julius Walker (1812-1899), Wasserbauingenieur (USA) In (hg. v. der American Society of Civil Engineers, ASCE): A biographical dictionary of American civil engineers, S. 1-2. New York. Agatz , Arnold (1891-1980), Hafenbauingenieur (D) Agricola , Georg (1494-1555), sächs. Arzt und Fachschriftsteller Aird , John (1833-1911), Wasserbauingenieur (GB) In: Dictionary of National Biographie, 2. Ergänz.-Bd. 1, S. 27-28. London. Alberti , Leon Battista (1404-1472), Architekt und Bauingenieur (I) Albrecht , Wilhelm (1785-1868), nass. Ingenieur des landwirtsch. Wasserbaus Stahl, K.-J., 1968: Albrecht, Wilhelm. In (hg. v. A. Stollenwerk): Kurzbiographien vom Mittelrhein und Moselland mit alphabetischen Namensregister Allemann , Franz (1838-1905), Wasserbauingenieur (CH) Aleotti , Giovanni Battista (um 1546-1636), Wasserbauingenieur (I) In: Thieme-Becker 1; S. 252-253; Koschlig, M., 1973: Wer war 'De La Grise'? In: Zeitschrift für Württembergische Landesgeschichte 32, S. 521-528.

75. Polski Dom Aukcyjny "SZTUKA" In Basilic Vatic. Anno 1740 Petrus bombelli Incid. Et Vendit Rom Anno Dom.1785. 200.. 47. Sadeler, rafael jr. ( 1584-1632 ) Swieta Rodzina , ok. http://www.sztuka.com.pl/historia/aukcj6.htm

HISTORIA - AUKCJA nr 6 Zapraszamy na aukcjê nr 6 10 pa¿dziernika 1998 Grafika, Rysunek , Akwarela do Pa³acu Larischa w Krakowie Pl. Wszystkich ¦w. 6. Pocz±tek o godz. 12.00 (nasza oferta poni¿ej). Wystawiane na sprzedaz obiekty mozna ogladac 8 i 9 pazdziernika w Palacu Sztuki w godz. 11.00 - 18.00 oraz w dniu aukcji w godz. 9.00 - 11.30 Bli¿sze informacje oraz zamówienia na katalogi prosimy sk³adaæ: Polski Dom Aukcyjny SZTUKA Pl. Wszystkich ¦w. 6, 31-004 Kraków e-mail sztuka@sztuka.com.pl Tel: (0-12) 429 14 13 Fax: (0-12)429 12 90 Zapraszamy do wspó³pracy kolekcjonerów i antykwariuszy. Przedmioty na aukcje przyjmujemy w naszej siedzibie na Placu Wszystkich ¦wiêtych 6 w Krakowie.

76. Colecciones De La Real Academía. Translate this page San Bruno - ESTEVE VILELLA, rafael. - San Diego de Alcalá. - NAVARRETEY FOS, Federico. - San Francisco de Paula - bombelli, Pedro. http://www.realacademiasancarlos.com/colecciones/Grabados/conten_gra.asp?NAV=7&Y

77. Raffael Bombelli Translate this page bombelli, Raffael. Raffael bombelli wurde am 20. Januar 1526 in derKathedrale San Pietro in Bologna getauft. In den Jahren vor 1560 http://www.mathe.tu-freiberg.de/~hebisch/cafe/bombelli.html

Bombelli, Raffael L'Algebra

78. Cerme 1 - Proceedings: Contents Vol. II REFLECTIONS AND EXAMPLES Giorgio T. Bagni bombelli's Algebra (1572)and Imaginary Numbers; Educational Problems The Focus of Our Work; http://www.fmd.uni-osnabrueck.de/ebooks/erme/cerme1-proceedings/cerme1_contents2

E uropean Society for R esearch in M athematics E ducation Institute for Cognitive Mathematics Contents Vol. II European Research in Mathematics Education I.I + I.II Proceedings of the First Conference of the European Society for Research in Mathematics Education Vol. I + II Editor: Inge Schwank, 1999 Publishing House: Forschungsinstitut fuer Mathematikdidaktik, Osnabrueck. Internet-Versions Vol. I: ISBN 3-925386-50-5 pdf-file 2.706 kB, V1.01 Vol. II: ISBN 3-925386-51-3 pdf-file 1.321 kB, V1.0 Paper-Versions Vol. I: ISBN: 3-925386-53-X how to order Vol. II: ISBN: 3-925386-54-8 how to order Overview including direct link to complete single contributions in pdf-format Vol. I: Table of contents I html-file Abstracts I html-file Vol. II:

79. Complex Numbers And Geometry A short time later, in 1572, another mathematician, rafael Bombellihelped to shape the nature of algebra for the next 400 years. http://campus.northpark.edu/math/PreCalculus/Transcendental/Trigonometric/Comple

Section 5.1: Complex Numbers and Geometry While the quadratic formula , has been known to give solutions to the quadratic equation, ax bx c = , since the time of the ancient Babylonian civilization (around 2000 BC), the simple looking equation, x + 1 = 0, was an enigma until relatively recently. That is because our number concept has historically been limited to those numbers which can be graphed on the real number line. In this section, we will see how the real number system is only a part of a larger number system, call the "complex" numbers. Moreover, we will see how the nice geometric interpretations of addition, multiplication, and negation of real numbers generalize to the complex numbers . We will also learn about a new operation, which applies to complex numbers, called conjugation , and discuss its geometric significance. The Origins of Complex Numbers For thousands of years, mathematicians considered the equation x + 1 = to be insolvable. From a functional point of view, we know that the range of the square function f x x , contains only positive numbers, so that

80. La Radice Quadrata http://digilander.libero.it/basecinque/scuola/radiquad.htm

BASE Cinque Il lato divertente della Matematica BASE Cinque Collezione Risposte La radice quadrata Rilassatevi, questo algoritmo è una ciliegina! La stima iniziale L'algoritmo Un altro esempio Spiegazione dell'algoritmo ... I consigli di Enrico Delfini Sorpresina! Digita un numero nella casella e clicca sul pulsante. Leggi qui il risultato. Esiste un metodo semplice per calcolare "a mano" la radice quadrata di un numero? Ne esistono diversi, ma non si può dire che siano semplicissimi. Il procedimento che viene ancora oggi insegnato nella scuola media è lo stesso che Rafael Bombelli presentò nella sua Opera su Algebra del 1550. Questo algoritmo è difficile da ricordare soprattutto se viene imparato meccanicamente, senza capirne le motivazioni. Gli strumenti per capirlo si acquisiscono nel primo anno della scuola superiore, con lo studio del calcolo letterale e dei cosiddetti prodotti notevoli. Gli antichi hanno faticato a lungo per costruire le tavole delle radici quadrate e i moderni hanno inventato le calcolatrici tascabili. Se il vostro obiettivo è risolvere dei problemi allora è meglio utilizzare le tavole o la calcolatrice.

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