O uso do ponto decimal é 1,5 século mais antigo do que os historiadores pensavam
Um historiador matemático da Trinity Wester University, no Canadá, descobriu o uso de um ponto decimal por um comerciante veneziano 150 anos antes de seu primeiro uso conhecido pelo matemático alemão Christopher Clavius.
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)
Da "Compositio instrumenti" de Bianchini. Reproduzido com permissão da Biblioteca Estense di Modena (Cod. Lat. 145, f. 7r). Crédito: História Matemática (2024). DOI: 10.1016/j.hm.2024.01.001
Um historiador matemático da Trinity Wester University, no Canadá, descobriu o uso de um ponto decimal por um comerciante veneziano 150 anos antes de seu primeiro uso conhecido pelo matemático alemão Christopher Clavius. Em seu artigo publicado na revista Historia Mathematica , Glen Van Brummelen descreve como encontrou evidências do uso decimal em um volume chamado “Tabulae” e seu significado para a história da matemática.
A invenção do ponto decimal levou ao desenvolvimento do sistema decimal e isso, por sua vez, tornou mais fácil para as pessoas que trabalham em vários campos calcular números não inteiros (frações) tão facilmente quanto números inteiros. Antes desta nova descoberta, o primeiro uso conhecido do ponto decimal foi feito por Christopher Clavius enquanto ele criava tabelas astronômicas – o trabalho resultante foi publicado em 1593.
A nova descoberta foi feita em parte de um manuscrito escrito por Giovanni Bianchini na década de 1440 – Van Brummelen estava discutindo uma seção de tabelas trigonométricas com um colega quando percebeu que alguns dos números incluíam um ponto no meio. Um exemplo foi 10,4, que Bianchini multiplicou por 8 da mesma forma que é feito com a matemática moderna. A descoberta mostra que um ponto decimal para representar números não inteiros ocorreu aproximadamente 150 anos antes do que se pensava anteriormente pelos historiadores da matemática.
Giovanni Bianchini trabalhou como comerciante em Veneza por muitos anos antes de ser nomeado para um cargo administrativo em uma importante propriedade de propriedade da poderosa família d'Este. Nessa função, ele também administrou ativos e investimentos, o que lhe conferiu uma sólida formação em matemática. Ele também publicou textos sobre astronomia, demonstrando sua capacidade de traçar o movimento planetário e de prever quando ocorreria um eclipse.
A descoberta sugere que Bianchini desempenhou um papel mais importante no desenvolvimento dos fundamentos da matemática do que se sabia anteriormente. Van Brummelen observa que, como comerciante, Bianchini teria viajado extensivamente, inclusive para lugares do mundo islâmico, onde conceitos matemáticos estavam sendo desenvolvidos, possivelmente influenciando seu uso de números não inteiros e formas de representá-los com mais facilidade.
Mais informações: Glen Van Brummelen, Numeração decimal fracionária e ponto decimal na Itália do século XV, Historia Mathematica (2024). DOI: 10.1016/j.hm.2024.01.001