Leseprobe
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Irrationality, Transcendence and the Circle-Squaring Problem
Eduardo Dorrego López, Elías Fuentes Guillén
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Springer International Publishing 
Naturwissenschaften, Medizin, Informatik, Technik / Allgemeines, Lexika
Beschreibung
This publication, now in its second edition, includes an unabridged and annotated translation of two works by Johann Heinrich Lambert (1728–1777) written in the 1760s: Vorläufige Kenntnisse für die, so die Quadratur und Rectification des Circuls suchen and Mémoire sur quelques propriétés remarquables des quantités transcendentes circulaires et logarithmiques. The translations, as in the first edition, are accompanied by a contextualised study of each of these works and provide an overview of Lambert’s contributions, showing both the background and the influence of his work. In addition, by adopting a biographical approach, it allows readers to better get to know the scientist himself.
Lambert was a highly relevant scientist and polymath in his time, admired by the likes of Kant, who despite having made a wide variety of contributions to different branches of knowledge, later faded into an undeserved secondary place with respect to other scientists of the eighteenth century. In mathematics, in particular, he is famous for his research on non-Euclidean geometries, although he is likely best known for having been the first who proved the irrationality of pi. In his Mémoire, he conducted one of the first studies on hyperbolic functions, offered a surprisingly rigorous proof of the irrationality of pi, established for the first time the modern distinction between algebraic and transcendental numbers, and based on such distinction, he conjectured the transcendence of pi and therefore the impossibility of squaring the circle.
Kundenbewertungen
Trascendental Numbers, Philosophy of Mathematics, The Circle-Squaring Problem, Lambert's Vorläufige Kenntnisse, Lambert and non-Euclidean geometry, Echegaray's Disertaciones matemáticas, Lambert's Mémoire, decimal expansions, History of Mathematics, Lambert's work and the development of irrational numbers, Continued Fractions, Lambert and the Berlin Academy of Sciences, 18th and 19th Century Mathematics, Johann Heinrich Lambert, Irrationality of Pi, Euler and continued fractions, irrationality and transcendence, Euler and continued fractions