Thomas Harriots Doctrine Of Triangular Numbers

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Thomas Harriot's Doctrine of Triangular Numbers

Author : Janet Beery
Publisher : European Mathematical Society
ISBN 13 : 9783037190593
Total Pages : 150 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis Thomas Harriot's Doctrine of Triangular Numbers by : Janet Beery

Download or read book Thomas Harriot's Doctrine of Triangular Numbers written by Janet Beery and published by European Mathematical Society. This book was released on 2009 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thomas Harriot (1560-1621) was a mathematician and astronomer who founded the English school of algebra. He is known not only for his work in algebra and geometry but also as a prolific writer with wide-ranging interests in ballistics, navigation, and optics. (He discovered the sine law of refraction now known as Snell's law.) By about 1614, Harriot had developed finite difference interpolation methods for navigational tables. In 1618 (or slightly later) he composed a treatise entitled `De numeris triangularibus et inde de progressionibus arithmeticis, Magisteria magna', in which he derived symbolic interpolation formulae and showed how to use them. This treatise was never published and is here reproduced for the first time. Commentary has been added to help the reader follow Harriot's beautiful but almost completely nonverbal presentation. The introductory essay preceding the treatise gives an overview of the contents of the `Magisteria' and describes its influence on Harriot's contemporaries and successors over the next sixty years. Harriot's method was not superseded until Newton, apparently independently, made a similar discovery in the 1660s. The ideas in the `Magisteria' were spread primarily through personal communication and unpublished manuscripts, and so, quite apart from their intrinsic mathematical interest, their survival in England during the seventeenth century provides an important case study in the dissemination of mathematics through informal networks of friends and acquaintances.

Thomas Harriot: Science and Discovery in the English Renaissance

Author : Robert Fox
Publisher : Taylor & Francis
ISBN 13 : 100081114X
Total Pages : 185 pages
Book Rating : 4.0/5 (8 download)

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Book Synopsis Thomas Harriot: Science and Discovery in the English Renaissance by : Robert Fox

Download or read book Thomas Harriot: Science and Discovery in the English Renaissance written by Robert Fox and published by Taylor & Francis. This book was released on 2022-12-29 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume sheds new light on one of the most remarkable polymaths of the English Renaissance. It offers original perspectives not only on Harriot’s personal achievements in mathematics and natural philosophy but also on the wider realms of exploration, colonial ambition, and philosophical debate in which he earned the attention and respect of contemporaries in and far beyond the socially elevated circles of his two great patrons, first Walter Ralegh and then Henry Percy, the ninth Earl of Northumberland. Harriot’s sixteenth-century world was one of unprecedented expansion in both scientific understanding and the discovery of new lands and peoples. The essays gathered here bring out forcefully the effect of this expanding vision, encapsulated in Harriot’s Briefe and true report of the new found land of Virginia (1588), the first detailed description of America to be published in the English language. In addition to an essay by a recent biographer of Harriot, the volume contains reworked versions of seven Thomas Harriot Lectures, an annual lecture series inaugurated in 1990 in Oriel College, Oxford. It follows two earlier volumes of Harriot Lectures, also edited by Robert Fox, that appeared in 2000 and 2012.

Thomas Harriot

Author : Robyn Arianrhod
Publisher : Oxford University Press
ISBN 13 : 0190271876
Total Pages : 478 pages
Book Rating : 4.1/5 (92 download)

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Book Synopsis Thomas Harriot by : Robyn Arianrhod

Download or read book Thomas Harriot written by Robyn Arianrhod and published by Oxford University Press. This book was released on 2019-04-04 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: As Robyn Arianrhod shows in this new biography, the most complete to date, Thomas Harriot was a pioneer in both the figurative and literal sense. Navigational adviser and loyal friend to Sir Walter Ralegh, Harriot--whose life was almost exactly contemporaneous to Shakespeare's--took part in the first expedition to colonize Virginia in 1585. Not only was he responsible for getting Ralegh's ships safely to harbor in the New World, he was also the first European to acquire a working knowledge of an indigenous language from what is today the US, and to record in detail the local people's way of life. In addition to his groundbreaking navigational, linguistic, and ethnological work, Harriot was the first to use a telescope to map the moon's surface, and, independently of Galileo, recorded the behavior of sunspots and discovered the law of free fall. He preceded Newton in his discovery of the properties of the prism and the nature of the rainbow, to name just two more of his unsung "firsts." Indeed many have argued that Harriot was the best mathematician of his age, and one of the finest experimental scientists of all time. Yet he has remained an elusive figure. He had no close family to pass down records, and few of his letters survive. Most importantly, he never published his scientific discoveries, and not long after his death in 1621 had all but been forgotten. In recent decades, many scholars have been intent on restoring Harriot to his rightful place in scientific history, but Arianrhod's biography is the first to pull him fully into the limelight. She has done it the only way it can be done: through his science. Using Harriot's re-discovered manuscripts, Arianrhod illuminates the full extent of his scientific and cultural achievements, expertly guiding us through what makes them original and important, and the story behind them. Harriot's papers provide unique insight into the scientific process itself. Though his thinking depended on a more natural, intuitive approach than those who followed him, and who achieved the lasting fame that escaped him, Harriot helped lay the foundations of what in Newton's time would become modern physics. Thomas Harriot: A Life in Science puts a human face to scientific inquiry in the Elizabethan and Jacobean worlds, and at long last gives proper due to the life and times of one of history's most remarkable minds.

Thomas Harriot and His World

Author : Robert Fox
Publisher : Routledge
ISBN 13 : 1351879197
Total Pages : 265 pages
Book Rating : 4.3/5 (518 download)

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Book Synopsis Thomas Harriot and His World by : Robert Fox

Download or read book Thomas Harriot and His World written by Robert Fox and published by Routledge. This book was released on 2016-12-05 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of papers on Thomas Harriot edited by Professor Robert Fox is based on the annual Harriot lectures delivered at Oriel College, Oxford between 2000 and 2009. It complements the previous volume, published as Thomas Harriot: An Elizabethan Man of Science in 2000. The focus in several of the papers is on Harriot's outstanding achievements as a mathematician; others consider why he has never received the recognition accorded to his great contemporary, Galileo; others again examine his association with his entrepreneurial patron Walter Ralegh and his contributions to the intensely practical world of exploration and seamanship, as exemplified in his voyage to the coast of present-day North Carolina in 1585. The volume adds significantly to our understanding of a true Renaissance man who wrote accomplished Latin, earned the respect of Europe's leading mathematicians and astronomers, and moved easily in circles close to the English court and whose 'Brief and true report of the new found land of Virginia' (1588) was the first detailed description of America to be published in the English language.

The Invention of Discovery, 1500–1700

Author : Dr James Dougal Fleming
Publisher : Ashgate Publishing, Ltd.
ISBN 13 : 1409478688
Total Pages : 240 pages
Book Rating : 4.4/5 (94 download)

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Book Synopsis The Invention of Discovery, 1500–1700 by : Dr James Dougal Fleming

Download or read book The Invention of Discovery, 1500–1700 written by Dr James Dougal Fleming and published by Ashgate Publishing, Ltd.. This book was released on 2013-05-28 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The early modern period used to be known as the Age of Discovery. More recently, it has been troped as an age of invention. But was the invention/discovery binary itself invented, or discovered? This volume investigates the possibility that it was invented, through a range of early modern knowledge practices, centered on the emergence of modern natural science. From Bacon to Galileo, from stagecraft to math, from martyrology to romance, contributors to this interdisciplinary collection examine the period's generation of discovery as an absolute and ostensibly neutral standard of knowledge-production. They further investigate the hermeneutic implications for the epistemological authority that tends, in modernity, still to be based on that standard. The Invention of Discovery, 1500–1700 is a set of attempts to think back behind discovery, considered as a decisive trope for modern knowledge.

The Doctrine of Triangles

Author : Glen Van Brummelen
Publisher : Princeton University Press
ISBN 13 : 0691179417
Total Pages : 390 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis The Doctrine of Triangles by : Glen Van Brummelen

Download or read book The Doctrine of Triangles written by Glen Van Brummelen and published by Princeton University Press. This book was released on 2021-06-08 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Series and Products in the Development of Mathematics: Volume 1

Author : Ranjan Roy
Publisher : Cambridge University Press
ISBN 13 : 1108573185
Total Pages : pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Series and Products in the Development of Mathematics: Volume 1 by : Ranjan Roy

Download or read book Series and Products in the Development of Mathematics: Volume 1 written by Ranjan Roy and published by Cambridge University Press. This book was released on 2021-03-18 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible to even advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 treats more recent work, including deBranges' solution of Bieberbach's conjecture, and requires more advanced mathematical knowledge.

Series and Products in the Development of Mathematics

Author : Ranjan Roy
Publisher : Cambridge University Press
ISBN 13 : 1108709370
Total Pages : 479 pages
Book Rating : 4.1/5 (87 download)

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Book Synopsis Series and Products in the Development of Mathematics by : Ranjan Roy

Download or read book Series and Products in the Development of Mathematics written by Ranjan Roy and published by Cambridge University Press. This book was released on 2021-03-18 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second of two volumes tracing the development of series and products. Second edition adds extensive material from original works.

Series and Products in the Development of Mathematics: Volume 2

Author : Ranjan Roy
Publisher : Cambridge University Press
ISBN 13 : 1108573150
Total Pages : 480 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Series and Products in the Development of Mathematics: Volume 2 by : Ranjan Roy

Download or read book Series and Products in the Development of Mathematics: Volume 2 written by Ranjan Roy and published by Cambridge University Press. This book was released on 2021-03-18 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible even to advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 examines more recent results, including deBranges' resolution of Bieberbach's conjecture and Nevanlinna's theory of meromorphic functions.

The Oxford Handbook of the History of Mathematics

Author : Eleanor Robson
Publisher : Oxford University Press on Demand
ISBN 13 : 0199213127
Total Pages : 927 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis The Oxford Handbook of the History of Mathematics by : Eleanor Robson

Download or read book The Oxford Handbook of the History of Mathematics written by Eleanor Robson and published by Oxford University Press on Demand. This book was released on 2009 with total page 927 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook explores the history of mathematics, addressing what mathematics has been and what it has meant to practise it. 36 self-contained chapters provide a fascinating overview of 5000 years of mathematics and its key cultures for academics in mathematics, historians of science, and general historians.

Commutation Relations, Normal Ordering, and Stirling Numbers

Author : Toufik Mansour
Publisher : CRC Press
ISBN 13 : 1466579897
Total Pages : 506 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Commutation Relations, Normal Ordering, and Stirling Numbers by : Toufik Mansour

Download or read book Commutation Relations, Normal Ordering, and Stirling Numbers written by Toufik Mansour and published by CRC Press. This book was released on 2015-09-18 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commutation Relations, Normal Ordering, and Stirling Numbers provides an introduction to the combinatorial aspects of normal ordering in the Weyl algebra and some of its close relatives. The Weyl algebra is the algebra generated by two letters U and V subject to the commutation relation UV - VU = I. It is a classical result that normal ordering pow

3000 Years of Analysis

Author : Thomas Sonar
Publisher : Springer Nature
ISBN 13 : 303058223X
Total Pages : 706 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis 3000 Years of Analysis by : Thomas Sonar

Download or read book 3000 Years of Analysis written by Thomas Sonar and published by Springer Nature. This book was released on 2020-12-27 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: What exactly is analysis? What are infinitely small or infinitely large quantities? What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals? You’ll find the answers to these and other questions in this unique book! It explains in detail the origins and evolution of this important branch of mathematics, which Euler dubbed the “analysis of the infinite.” A wealth of diagrams, tables, color images and figures serve to illustrate the fascinating history of analysis from Antiquity to the present. Further, the content is presented in connection with the historical and cultural events of the respective epochs, the lives of the scholars seeking knowledge, and insights into the subfields of analysis they created and shaped, as well as the applications in virtually every aspect of modern life that were made possible by analysis.

Sources in the Development of Mathematics

Author : Ranjan Roy
Publisher : Cambridge University Press
ISBN 13 : 1139497758
Total Pages : 1139 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Sources in the Development of Mathematics by : Ranjan Roy

Download or read book Sources in the Development of Mathematics written by Ranjan Roy and published by Cambridge University Press. This book was released on 2011-06-13 with total page 1139 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discovery of infinite products by Wallis and infinite series by Newton marked the beginning of the modern mathematical era. It allowed Newton to solve the problem of finding areas under curves defined by algebraic equations, an achievement beyond the scope of the earlier methods of Torricelli, Fermat and Pascal. While Newton and his contemporaries, including Leibniz and the Bernoullis, concentrated on mathematical analysis and physics, Euler's prodigious accomplishments demonstrated that series and products could also address problems in algebra, combinatorics and number theory. In this book, Ranjan Roy describes many facets of the discovery and use of infinite series and products as worked out by their originators, including mathematicians from Asia, Europe and America. The text provides context and motivation for these discoveries, with many detailed proofs, offering a valuable perspective on modern mathematics. Mathematicians, mathematics students, physicists and engineers will all read this book with benefit and enjoyment.

Dense Sphere Packings

Author : Thomas Hales
Publisher : Cambridge University Press
ISBN 13 : 113957647X
Total Pages : 286 pages
Book Rating : 4.1/5 (395 download)

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Book Synopsis Dense Sphere Packings by : Thomas Hales

Download or read book Dense Sphere Packings written by Thomas Hales and published by Cambridge University Press. This book was released on 2012-09-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 400-year-old Kepler conjecture asserts that no packing of congruent balls in three dimensions can have a density exceeding the familiar pyramid-shaped cannonball arrangement. In this book, a new proof of the conjecture is presented that makes it accessible for the first time to a broad mathematical audience. The book also presents solutions to other previously unresolved conjectures in discrete geometry, including the strong dodecahedral conjecture on the smallest surface area of a Voronoi cell in a sphere packing. This book is also currently being used as a blueprint for a large-scale formal proof project, which aims to check every logical inference of the proof of the Kepler conjecture by computer. This is an indispensable resource for those who want to be brought up to date with research on the Kepler conjecture.

The Mathematical Writings of Évariste Galois

Author : Évariste Galois
Publisher : European Mathematical Society
ISBN 13 : 9783037191040
Total Pages : 426 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis The Mathematical Writings of Évariste Galois by : Évariste Galois

Download or read book The Mathematical Writings of Évariste Galois written by Évariste Galois and published by European Mathematical Society. This book was released on 2011 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Before he died at the age of twenty, shot in a mysterious early-morning duel at the end of May 1832, Evariste Galois created mathematics that changed the direction of algebra. This book contains English translations of almost all the Galois material. The translations are presented alongside a new transcription of the original French and are enhanced by three levels of commentary. An introduction explains the context of Galois' work, the various publications in which it appears, and the vagaries of his manuscripts. Then there is a chapter in which the five mathematical articles published in his lifetime are reprinted. After that come the testamentary letter and the first memoir (in which Galois expounded on the ideas that led to Galois Theory), which are the most famous of the manuscripts. These are followed by the second memoir and other lesser known manuscripts. This book makes available to a wide mathematical and historical readership some of the most exciting mathematics of the first half of the nineteenth century, presented in its original form. The primary aim is to establish a text of what Galois wrote. The details of what he did, the proper evidence of his genius, deserve to be well understood and appreciated by mathematicians as well as historians of mathematics.

Pangeometry

Author : Nikolaĭ Ivanovich Lobachevskiĭ
Publisher : European Mathematical Society
ISBN 13 : 9783037190876
Total Pages : 332 pages
Book Rating : 4.1/5 (98 download)

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Book Synopsis Pangeometry by : Nikolaĭ Ivanovich Lobachevskiĭ

Download or read book Pangeometry written by Nikolaĭ Ivanovich Lobachevskiĭ and published by European Mathematical Society. This book was released on 2010 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lobachevsky wrote Pangeometry in 1855, the year before his death. This memoir is a resume of his work on non-Euclidean geometry and its applications and can be considered his clearest account on the subject. It is also the conclusion of his life's work and the last attempt he made to acquire recognition. The treatise contains basic ideas of hyperbolic geometry, including the trigonometric formulae, the techniques of computation of arc length, of area and of volume, with concrete examples. It also deals with the applications of hyperbolic geometry to the computation of new definite integrals. The techniques are different from those found in most modern books on hyperbolic geometry since they do not use models. Besides its historical importance, Lobachevsky's Pangeometry is a beautiful work, written in a simple and condensed style. The material that it contains is still very alive, and reading this book will be most useful for researchers and for students in geometry and in the history of science. It can be used as a textbook, as a sourcebook, and as a repository of inspiration. The present edition provides the first complete English translation of Pangeometry available in print. It contains facsimiles of both the Russian and the French original versions. The translation is accompanied by notes, followed by a biography of Lobachevky and an extensive commentary.

From Cardano's Great Art to Lagrange's Reflections

Author : Jacqueline A. Stedall
Publisher : European Mathematical Society
ISBN 13 : 9783037190920
Total Pages : 244 pages
Book Rating : 4.1/5 (99 download)

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Book Synopsis From Cardano's Great Art to Lagrange's Reflections by : Jacqueline A. Stedall

Download or read book From Cardano's Great Art to Lagrange's Reflections written by Jacqueline A. Stedall and published by European Mathematical Society. This book was released on 2011 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an exploration of a claim made by Lagrange in the autumn of 1771 as he embarked upon his lengthy ``Reflexions sur la resolution algebrique des equations'': that there had been few advances in the algebraic solution of equations since the time of Cardano in the mid sixteenth century. That opinion has been shared by many later historians. The present study attempts to redress that view and to examine the intertwined developments in the theory of equations from Cardano to Lagrange. A similar historical exploration led Lagrange himself to insights that were to transform the entire nature and scope of algebra. Progress was not confined to any one country: at different times mathematicians in Italy, France, the Netherlands, England, Scotland, Russia, and Germany contributed to the discussion and to a gradual deepening of understanding. In particular, the national Academies of Berlin, St. Petersburg, and Paris in the eighteenth century were crucial in supporting informed mathematical communities and encouraging the wider dissemination of key ideas. This study therefore truly highlights the existence of a European mathematical heritage. The book is written in three parts. Part I offers an overview of the period from Cardano to Newton (1545 to 1707) and is arranged chronologically. Part II covers the period from Newton to Lagrange (1707 to 1771) and treats the material according to key themes. Part III is a brief account of the aftermath of the discoveries made in the 1770s. The book attempts throughout to capture the reality of mathematical discovery by inviting the reader to follow in the footsteps of the authors themselves, with as few changes as possible to the original notation and style of presentation.