Luca Pacioli

​Luca Pacioli aka Fra luca di Borga

Profile of a Mathematician​

​​Nationality

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​1445 - 1517

​​Years of Life

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Multiple Choice

What is the nationality of Luca Pacioli?

• French

• German

• Italian

• Swiss

Multiple Choice

Luca lived from 1445 to 1517. How many years did he live?

• 70

• 71

• 72

• 73

​solving cubic equations

​​Algebra

​game of chance

​​Probability

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​​Major mathematical interests and contributions to Mathematics

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​1470: dedicated to Rompiasi’s three sons, 1477-1480: University of Perugia classes, Zara or Jadera in Croatia

​​unpublished three arithmetic texts

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​1494; 600-page work written in the Tuscan dialect

​​Summa de arithmetica, geometria, proportioni et proportionalita / summary of arithmetic, geometry,  and algebra

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​​Publications

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​1509; geometry, accompanied by a set of wooden figures intended to reinforce learning

​​De Divina Proportione

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​1496-1508, written to enliven the evenings at court and to sharpen the wits to solve mysterious problems and arithmetic and geometric puzzles

​​De Viribus Quantitus / On the Powers of Numbers

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​​Publications

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​1500; a book of chess puzzles intended to teach the latest form of the game

​​De Ludo Scachorum / On the Game of Chess

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​​Publications

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Multiple Choice

Which material is considered as the greatest contribution of Luca Pacioli?

• Summa de arithmetica, geometria, proportioni et proportionalita

• De Divina Proportione

• De Viribus Quantitus

• De Ludo Scachorum

​​Father of Accounting

​​consultant on military tactics to advisors to the King of Naples

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​recognized at the highest level of society by being appointed astrologer (mathematician) to Pope Leo X

​Pacioli ended his Summa by asserting that the solution of the cubic equation was as impossible as the quadrature of the circle. This put off some mathematicians from the attempt but only induced others to try. In the first or second decade of the sixteenth century, Scipione del Ferro (1465–1526) of the University of Bologna shattered Pacioli’s prediction by solving the cubic equation for the special case x³ + px = q, where p and q are positive. Pacioli may have personally stimulated this first great achievement of Renaissance algebra, for in 1501–1502 he lectured at the University of Bologna, where one of his colleagues was del Ferro.

​As part of his teaching, Pacioli composed three different abacus texts for his students. He regretted what he believed to be the low ebb to which teaching had fallen. Because he felt that one of the problems was the scarcity of available subject material, he gathered mathematical materials for some twenty years and in 1494 completed the most comprehensive mathematics text of the time, and one of the earliest mathematics texts to be printed.

Fill in the Blanks

A team plays ball so that a total of 60 points is required to win the game and the stakes are 22 ducats. By some incident, they cannot finish the game and one side has 50 points, and the other 30. What share of the prize money belongs to each side?