The Impossibility Of Squaring The Circle In The 17th Century
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The Impossibility Of Squaring The Circle In The 17th Century
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Author : Davide Crippa
language : en
Publisher: Springer
Release Date : 2019-03-06
The Impossibility Of Squaring The Circle In The 17th Century written by Davide Crippa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-06 with Mathematics categories.
This book is about James Gregory’s attempt to prove that the quadrature of the circle, the ellipse and the hyperbola cannot be found algebraically. Additonally, the subsequent debates that ensued between Gregory, Christiaan Huygens and G.W. Leibniz are presented and analyzed. These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise on the arithmetical quadrature of the circle. The author shows how the controversy around the possibility of solving the quadrature of the circle by certain means (algebraic curves) pointed to metamathematical issues, particularly to the completeness of algebra with respect to geometry. In other words, the question underlying the debate on the solvability of the circle-squaring problem may be thus phrased: can finite polynomial equations describe any geometrical quantity? As the study reveals, this question was central in the early days of calculus, when transcendental quantities and operations entered the stage. Undergraduate and graduate students in the history of science, in philosophy and in mathematics will find this book appealing as well as mathematicians and historians with broad interests in the history of mathematics.
Bruce Nauman
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Author : Adi Louria Hayon
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-05-06
Bruce Nauman written by Adi Louria Hayon and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-06 with Religion categories.
To date, scholars explored Bruce Nauman’s oeuvre through various perspectives, concepts and premises, including linguistics, performance, power and knowledge, sound, the political and more. Amidst this vast and rich field, Nauman’s pieces have been regarded by critics in terms of systematic skepticism, tragic skepticism, skepticism of the medium, and linguistic doubt. This book methodically analyzes the notion of performative skepticism and its relevance to various dimensions of Bruce Nauman’s post-minimalist artistic practice. It is argued that Nauman performs the perpetual failure of perception, hence, demonstrating its doubtful validity to produce certain knowledge without allowing a resolution. This kind of skepticism, here called performative skepticism, exposes the impossibility of epistemological equipment to produce knowledge, and the impossibility of attaining certainty in bridging the gap between knowledge and the real.
A History Of Mathematical Impossibility
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Author : Jesper Lützen
language : en
Publisher: Oxford University Press
Release Date : 2023
A History Of Mathematical Impossibility written by Jesper Lützen and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Mathematics categories.
This book tells the history of impossibility theorems starting with the ancient Greek proof of the incommensurability of the side and the diagonal in a square.
The Doctrine Of Triangles
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Author : Glen Van Brummelen
language : en
Publisher: Princeton University Press
Release Date : 2025-06-17
The Doctrine Of Triangles written by Glen Van Brummelen and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-17 with Mathematics categories.
An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry’s participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms. A masterful combination of scholarly rigor and compelling narrative, The Doctrine of Triangles brings trigonometry’s rich historical past full circle into the modern era.
Leibniz On Binary
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Author : Lloyd Strickland
language : en
Publisher: MIT Press
Release Date : 2022-10-25
Leibniz On Binary written by Lloyd Strickland and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-25 with Mathematics categories.
The first collection of Leibniz’s key writings on the binary system, newly translated, with many previously unpublished in any language. The polymath Gottfried Wilhelm Leibniz (1646–1716) is known for his independent invention of the calculus in 1675. Another major—although less studied—mathematical contribution by Leibniz is his invention of binary arithmetic, the representational basis for today’s digital computing. This book offers the first collection of Leibniz’s most important writings on the binary system, all newly translated by the authors with many previously unpublished in any language. Taken together, these thirty-two texts tell the story of binary as Leibniz conceived it, from his first youthful writings on the subject to the mature development and publication of the binary system. As befits a scholarly edition, Strickland and Lewis have not only returned to Leibniz’s original manuscripts in preparing their translations, but also provided full critical apparatus. In addition to extensive annotations, each text is accompanied by a detailed introductory “headnote” that explains the context and content. Additional mathematical commentaries offer readers deep dives into Leibniz’s mathematical thinking. The texts are prefaced by a lengthy and detailed introductory essay, in which Strickland and Lewis trace Leibniz’s development of binary, place it in its historical context, and chart its posthumous influence, most notably on shaping our own computer age.
Leibniz In His World
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Author : Audrey Borowski
language : en
Publisher: Princeton University Press
Release Date : 2024-11-12
Leibniz In His World written by Audrey Borowski and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-12 with Biography & Autobiography categories.
A sweeping intellectual biography that restores the Enlightenment polymath to the intellectual, scientific, and courtly worlds that shaped his early life and thought Described by Voltaire as “perhaps a man of the most universal learning in Europe,” Gottfried Wilhelm Leibniz (1646–1716) is often portrayed as a rationalist and philosopher who was wholly detached from the worldly concerns of his fellow men. Leibniz in His World provides a groundbreaking reassessment of Leibniz, telling the story of his trials and tribulations as an aspiring scientist and courtier navigating the learned and courtly circles of early modern Europe and the Republic of Letters. Drawing on extensive correspondence by Leibniz and many leading figures of the age, Audrey Borowski paints a nuanced portrait of Leibniz in the 1670s, during his “Paris sojourn” as a young diplomat and in Germany at the court of Duke Johann Friedrich of Hanover. She challenges the image of Leibniz as an isolated genius, revealing instead a man of multiple identities whose thought was shaped by a deep engagement with the social and intellectual milieus of his time. Borowski shows us Leibniz as he was known to his contemporaries, enabling us to rediscover him as an enigmatic young man who was complex and all too human. An exhilarating work of scholarship, Leibniz in His World demonstrates how this uncommon intellect, torn between his ideals and the necessity to work for absolutist states, struggled to make a name for himself during his formative years.
Leibniz S Correspondence In Science Technology And Medicine 1676 1701
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Author : James O'Hara
language : en
Publisher: BRILL
Release Date : 2024-07-29
Leibniz S Correspondence In Science Technology And Medicine 1676 1701 written by James O'Hara and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-29 with Science categories.
Leibniz’s correspondence from his years spent in Paris (1672-1676) reflects his growth to mathematical maturity whereas that from the years 1676-1701 reveals his growth to maturity in science, technology and medicine in the course of which more than 2000 letters were exchanged with more than 200 correspondents. The remaining years until his death in 1716 witnessed above all the appearance of his major philosophical works. The focus of the present work is Leibniz's middle period and the core themes and core texts from his multilingual correspondence are presented in English from the following subject areas: mathematics, natural philosophy, physics (and cosmology), power technology (including mining and transport), engineering and engineering science, projects (scientific, technological and economic projects), alchemy and chemistry, geology, biology and medicine.
Beyond The Learned Academy
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Author : Philip Beeley
language : en
Publisher: Oxford University Press
Release Date : 2024
Beyond The Learned Academy written by Philip Beeley and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with History categories.
Comprising fifteen essays by leading authorities in the history of mathematics, this volume aims to exemplify the richness, diversity, and breadth of mathematical practice from the seventeenth century through to the middle of the nineteenth century.
Comprehending The Complexity Of Countries
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Author : Hans Kuijper
language : en
Publisher: Springer Nature
Release Date : 2022-01-18
Comprehending The Complexity Of Countries written by Hans Kuijper and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-18 with Social Science categories.
This book argues for computer-aided collaborative country research based on the science of complex and dynamic systems. It provides an in-depth discussion of systems and computer science, concluding that proper understanding of a country is only possible if a genuinely interdisciplinary and truly international approach is taken; one that is based on complexity science and supported by computer science. Country studies should be carefully designed and collaboratively carried out, and a new generation of country students should pay more attention to the fast growing potential of digitized and electronically connected libraries. In this frenzied age of globalization, foreign policy makers may – to the benefit of a better world – profit from the radically new country studies pleaded for in the book. Its author emphasizes that reductionism and holism are not antagonistic but complementary, arguing that parts are always parts of a whole and a whole has always parts.
The Palgrave Handbook Of Literature And Mathematics
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Author : Robert Tubbs
language : en
Publisher: Springer Nature
Release Date : 2020-12-30
The Palgrave Handbook Of Literature And Mathematics written by Robert Tubbs and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-30 with Literary Criticism categories.
This handbook features essays written by both literary scholars and mathematicians that examine multiple facets of the connections between literature and mathematics. These connections range from mathematics and poetic meter to mathematics and modernism to mathematics as literature. Some chapters focus on a single author, such as mathematics and Ezra Pound, Gertrude Stein, or Charles Dickens, while others consider a mathematical topic common to two or more authors, such as squaring the circle, chaos theory, Newton’s calculus, or stochastic processes. With appeal for scholars and students in literature, mathematics, cultural history, and history of mathematics, this important volume aims to introduce the range, fertility, and complexity of the connections between mathematics, literature, and literary theory. Chapter 1 is available open access under a Creative Commons Attribution 4.0 International License via [link.springer.com|http://link.springer.com/].