quaternions: sucessos e insucessos de um projeto de pesquisa
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ID: 227311
1995
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Abstract
Neste artigo, são examinadas as investigações do matemático William Rowan Hamilton que conduziram à caracterização de certos objetos matemáticos chamados Quaternions, entre 1843 e 1866. Embora tais objetos tenham gerado muitas expectativas de utilização, sobretudo no que se refere à síntese sugerida entre grandezas escalares e vetoriais, quase todas resultaram frustradas em relativamente pouco tempo, tendo entrado em cena outros instrumentos que se revelaram mais fecundos, como os tensores, por exemplo. As investigações de Hamilton, no entanto, contribuíram significativamente para o desenvolvimento da Álgebra e a leitura de seus textos originais pode evidenciar a importância do recurso à História da Ciência para instrumentar a prática pedagógica, especialmente no que tange à Matemática e à Física.
This article examines the mathematical works of William Rowan Hamilton that led him to characterize certain mathematical objects named Quaternions, in the years between 1843 and 1866. Many expectations about practical applications of the Quaternions were posed, specially the challenge of synthesize the representation of scalar and vector magnitudes; howewer, few years later, these expectations were frustated, and new kinds of powerful instruments came out in mathematical scene, like tensors, for instance. Hamilton's researches, nevertheless, contributed vividly to Algebra's development, underlining the meaning of several algebrical themes. There is another reason to read Hamilton's works in their original form: exploring life and death of the Quaternions, the importance of History of Science becomes evident, in order to instruct and guide pedagogical actions, specially in mathematical and physical themes.
This article examines the mathematical works of William Rowan Hamilton that led him to characterize certain mathematical objects named Quaternions, in the years between 1843 and 1866. Many expectations about practical applications of the Quaternions were posed, specially the challenge of synthesize the representation of scalar and vector magnitudes; howewer, few years later, these expectations were frustated, and new kinds of powerful instruments came out in mathematical scene, like tensors, for instance. Hamilton's researches, nevertheless, contributed vividly to Algebra's development, underlining the meaning of several algebrical themes. There is another reason to read Hamilton's works in their original form: exploring life and death of the Quaternions, the importance of History of Science becomes evident, in order to instruct and guide pedagogical actions, specially in mathematical and physical themes.
| Reference Key |
dion1995estudosquaternions:
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| Authors | ;Sonia Maria Dion;Jesuína Lopes de Almeida Pacca;Nilson José Machado |
| Journal | journal of theoretical and applied information technology |
| Year | 1995 |
| DOI |
10.1590/S0103-40141995000300019
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