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Renaissance

Renaissance. The development of mathematics almost stopped between the fourteenth century and the first half of the fifteenth century. Faced with unfavorable social and economic environment, the learned world could hardly devote its energy to intellectual development.

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Renaissance

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  1. Renaissance

  2. The development of mathematics almost stopped between the fourteenth century and the first half of the fifteenth century.

  3. Faced with unfavorable social and economic environment, the learned world could hardly devote its energy to intellectual development.

  4. The growth of mathematics was not only retarded by war, but also by the injurious influence of traditional scholastic philosophy. Mathematicians could hardly receive respect from scholars of other disciplines.

  5. There were few jobs in universities for mathematicians. At some universities, the curriculum requirement of mathematical learning had not changed for almost two centuries since the fourteenth

  6. A change gradually appeared with the beginning of the mid- fifteenth century.

  7. Mathematicians now were able to, and wanted to, study original Latin and Greek works. They translated many Greek mathematics textbooks.

  8. Euclid's great book Elements was also translated.

  9. the mathematicians eventually went beyond the Greek knowledge. They expanded their knowledge along with the increasing practical needs for mathematics.

  10. The Renaissance scholars slowly drifted away from the old scholastic leanings. They began to prefer scientific inquiry and experiments

  11. Factors contributing to mathematical development New printing technology

  12. New printing technology was introduced in Europe A rag paper process was developed Now, many people could afford to have books The growing social and economic activities encouraged the study of mathematics The need for mathematical knowledge of making maps Germany(astronomy and trigonometry)and Italy(algebra)made major contributions to Renaissance mathematics

  13. Progress in arithmetics. Practical uses of arithmetics. • The development of commercial activities • Shopkeepers, numerous mercantile businesses required computation methods • teachers taught commercial arithmetic at business schools for training future traders.

  14. The earliest arithmetic book was printed in Italy in 1478 • In 1582, an arithmetician, Fleming Simon Stevin, for the first time published a book containing interest tables along with the method for computing them.

  15. Old and new methods of multiplication. • An older way of multiplication, which was used in 1424 that can be demonstrated by an example of 34*45 4 5 34 20 16 15 12 1530

  16. By 1494, the present chessboard method of multiplication was invented 9437 28 75496 18874 264236

  17. Solutions to cubic equations • At the time of the Renaissance, there were no general formulas to solve cubic and fourth degree equations • In Renaissance, mathematicians were able to make considerable progress in solving some specific types of cubics

  18. First solution of cubic equation • given by Scipione del Ferro, professor of mathematics in Bologna • Not much is known about his solutions because he didn't publicize his result

  19. A contest on solving cubic equation • Nicollo Fontana (Tartaglia, 1500. – 1557.) vs. Antonio Maria Fior • public contest in solving 30 mathematician problems • winner was Tartaglia, because he found general formula of solving cubic equation, and Fior only knew how to solve one special case

  20. General formula of solving cubic equation • With modern notations, we would write that, to find of solution of: • we only need to find t,u such that and • Then: • The values of t and u are easily found: • therefore, the solution of given cubic equation is: and

  21. Girolamo Cardano (1501. – 1576.) • successful scientist who wrote a number of books on a wide variety of subjects • He asked Tartaglia to give him his solution. Although he refused at first, afer some time Tartaglia send Cardano a poem in Italian which describes procedure of solving cubic equation. • Cardano and his assistant Ludovico Ferrari • found justifications for the Tartaglia's formulas • solved all the other types of cubics • solved the quartic equation • Cardano solved and published it in Ars Magna.

  22. Expressing mathematician problems What changed? abbreviations were standardized mathematicians were able to classify solutions to problems (generalization) modern symbol Use of symbolism and its benefits • Before: • rhetorically, or by a combination of verbalized statements and abbreviations for often used concepts and operators • abbreviations were not standardized • lack of uniformity in symbols

  23. Regiomontatus: a typical "Renaissance man"

  24. Regiomontatus' contribution to trigonometry • His real name was Johannes Müller von Königsberg (1436-1476) • He was born in Germany • Perhaps the most capable mathematician of his time • His main contribution to mathematics was in trigonometry (he separated it from astronomy) • His book De Triangulis - the first great book on trigonometry to appear in print

  25. Discovered for the first time the relationship between sides and angles of a triangle • Invented the mathematical concept of the tangent and created a table of tangents

  26. Regiomontatus' interest in humanistic learning • Regiomontatus spent many years learning classic Latin so he could translate the great Greek mathematics book Almagest into Latin • He was interested in humanistic learning and worked at the University of Vienna by (teached humanities)

  27. Istance of Columbus using Regiomontatus' book • Columbus once predicted that a total eclipse of the moon would occur in February 29, 1504 • After the prediction came true, Columbus took advantage of it and frightened the Indians to obey him and to provide food for his ships

  28. Mathematical influences on art

  29. Renaissance art differed from art in the Middle ages in many ways, i.e. the objects in paintings were flat and more symbolic than real in appearance • Renaissance artists tried to reform the old style of painting - they wanted objects in paintings to be represented with perfection and accuracy • Several mathematically inclined artists began to study the geometry of perspective

  30. Leonardo da Vinci (1452-1519)

  31. The visual scenes of Renaissance art were represented with much more overlapping • The objects were more often painted in three dimensional perspective • The first book concerning the application of mathematical knowledge to art was published in 1435

  32. Magic square • A writer, Manuel Moschopulus is believed to be responsible for introducing the magic square into Europe • A magic square is an n*n square which consists of integer numbers starting from 1 to n2 • The numbers in the square are arranged in a way that the sum of all rows, columns and two diagonals are the same • Astrologers and physicians believed that there was some mystical power contained in the magic square and people considered it as a charm against epidemics

  33. Ljiljana Pujić Marta Pušić Anamarija Repić Matea Nosse Antun Vidić

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