From Discrete to Continuous

K. Neal

ISBN 10: 1402005652 / ISBN 13: 9781402005657

Editore: Springer Netherlands, Springer Netherlands Apr 2002, 2002

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Neuware -In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways.This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 192 pp. Englisch.

Codice articolo 9781402005657

Dati bibliografici

• Titolo: From Discrete to Continuous
• Editore: Springer Netherlands, Springer Netherlands Apr 2002
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 1402005652
• ISBN 13: 9781402005657
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 16 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 16 millimetri di profondità
• Peso: 459 grammi

Descrizione articolo

Riassunto

In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways.

This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.

Contenuti

Acknowledgments. 1. Transformation of the Number Concept. 2. The Ancient Sources. 3. The Contemporary Infuences. 4. Early Modern English Algebra. 5. The Development of the Logarithms: Napier and Briggs. 6. Isaac Barrow. 7. John Wallis. 8. Conclusion. References. Indices.