L'Algebra. Rafael Bombelli , Federigo Enriques

“Keep an open mind, because imaginary numbers exist” offers a basic introduction to imaginary numbers, including their history and some real-life applications. In the 1500s, Italian mathematician Rafael Bombelli considered the possibility that an equation such as had a solution. Later, in the 1600s, Rene Descartes defined a new number with the property. He selected the letter for “imaginary”—a word that betrayed his discomfort with the idea. The number is a solution to the equation. In general, an imaginary number may be written as, where and are real numbers and. Mathematics students and enthusiasts who feel bewildered by any mathematical concept are encouraged to work to uncover mysteries in mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

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Um breve histórico da resolução das equações algébricas de grau 3

Revista Dissertar ◽

10.24119/16760867ed11148 ◽

2015 ◽

Vol 1 (22 e 23) ◽

pp. 51-56

Author(s):

Carlos Alberto Martins de Assis

Keyword(s):

Rafael Bombelli

Na Matemática a teoria dasequações algébricas é de relevânciaindiscutível. Assim, neste artigo, faremos uma exposição histórica doproblema da resolução de equaçõesalgébricas com coefcientes reais (degrau 3), desde os antigos babilôniospassando pelas civilizações grega,árabe e chinesa até chegarmos àscontribuições de alguns matemáticositalianos como, por exemplo, GerônimoCardano, o brilhante mau-caráter;Niccolò de Brescia (Tartaglia) o pobremenino autodidata e Rafael Bombelli,o destemido manipulador dos númeroscomplexos. Comentaremos que na Gré-cia Clássica, problemas de enunciadosmuitos simples como, a duplicação docubo e a trissecção do ângulo, fcaramfamosos pela impossibilidade de seremresolvidos usando exclusivamente a ré-gua não-graduada e o compasso, e queao longo dos tempos e em particular noperíodo helênico (compreendido entreo século VI a.C. e o século V d. C.), setornaram uma fonte rica de idéias eprocessos matemáticos.

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Rafael Bombelli, Engineer-Architect: Some Unpublished Documents of the Apostolic Camera

Isis ◽

10.1086/349998 ◽

1965 ◽

Vol 56 (3) ◽

pp. 298-306 ◽

Cited By ~ 4

Author(s):

S. A. Jayawardene

Keyword(s):

Rafael Bombelli

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Hierarchies of Dignity

Enlightening Symbols ◽

10.23943/princeton/9780691173375.003.0014 ◽

2016 ◽

Author(s):

Joseph Mazur

Keyword(s):

English Word ◽

Roots Of Polynomials ◽

Factoring Polynomials ◽

Rafael Bombelli

This chapter discusses what Rafael Bombelli called dignità, which translates to the English word “dignity” and is equivalent to what we refer to as “exponents.” It first considers Bombelli's L'Algebra (1579), which introduces a new kind of notation for the unknown and its powers. Written in Italian, L'Algebra used equality in a different sense than we do. For Bombelli, the higher powers meant hierarchies of dignity. He was not only inventing genuine symbols when depicting dignità as little cups holding numbers, but also inventing words that were new to mathematics. The chapter also examines how the problem of finding the roots of polynomials became the problem of factoring polynomials. Finally, it looks at René Descartes's idea of using numerical superscripts to mark positive integral exponents of a polynomial in his La Géométrie.

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The Influence of Practical Arithmetics on the Algebra of Rafael Bombelli

Isis ◽

10.1086/351179 ◽

1973 ◽

Vol 64 (4) ◽

pp. 510-523 ◽

Cited By ~ 10

Author(s):

S. A. Jayawardene ◽

Di Rafael Bombelli

Keyword(s):

Rafael Bombelli

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