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Author : Thomas L. Heath
Publisher : CUP Archive
Page : 406 pages
File Size : 43,7 Mb
Release : 1910
Category : Algebra
ISBN : 8210379456XXX
Author : Jacques Sesiano
Publisher : Springer Science & Business Media
Page : 507 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461381747
This edition of Books IV to VII of Diophantus' Arithmetica, which are extant only in a recently discovered Arabic translation, is the outgrowth of a doctoral dissertation submitted to the Brown University Department of the History of Mathematics in May 1975. Early in 1973, my thesis adviser, Gerald Toomer, learned of the existence of this manuscript in A. Gulchln-i Macanl's just-published catalogue of the mathematical manuscripts in the Mashhad Shrine Library, and secured a photographic copy of it. In Sep tember 1973, he proposed that the study of it be the subject of my dissertation. Since limitations of time compelled us to decide on priorities, the first objective was to establish a critical text and to translate it. For this reason, the Arabic text and the English translation appear here virtually as they did in my thesis. Major changes, however, are found in the mathematical com mentary and, even more so, in the Arabic index. The discussion of Greek and Arabic interpolations is entirely new, as is the reconstruction of the history of the Arithmetica from Diophantine to Arabic times. It is with the deepest gratitude that I acknowledge my great debt to Gerald Toomer for his constant encouragement and invaluable assistance.
Author : Isabella Grigoryevna Bashmakova
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 42,5 Mb
Release : 2019-01-29
Category : Mathematics
ISBN : 9781470450496
This book tells the story of Diophantine analysis, a subject that, owing to its thematic proximity to algebraic geometry, became fashionable in the last half century and has remained so ever since. This new treatment of the methods of Diophantus--a person whose very existence has long been doubted by most historians of mathematics--will be accessible to readers who have taken some university mathematics. It includes the elementary facts of algebraic geometry indispensable for its understanding. The heart of the book is a fascinating account of the development of Diophantine methods during the.
Author : Titu Andreescu,Dorin Andrica,Ion Cucurezeanu
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 47,8 Mb
Release : 2010-09-02
Category : Mathematics
ISBN : 9780817645496
This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.
Author : Daniel Coray
Publisher : Springer Nature
Page : 186 pages
File Size : 48,8 Mb
Release : 2020-07-06
Category : Mathematics
ISBN : 9783030437817
This English translation of Daniel Coray’s original French textbook Notes de géométrie et d’arithmétique introduces students to Diophantine geometry. It engages the reader with concrete and interesting problems using the language of classical geometry, setting aside all but the most essential ideas from algebraic geometry and commutative algebra. Readers are invited to discover rational points on varieties through an appealing ‘hands on’ approach that offers a pathway toward active research in arithmetic geometry. Along the way, the reader encounters the state of the art on solving certain classes of polynomial equations with beautiful geometric realizations, and travels a unique ascent towards variations on the Hasse Principle. Highlighting the importance of Diophantus of Alexandria as a precursor to the study of arithmetic over the rational numbers, this textbook introduces basic notions with an emphasis on Hilbert’s Nullstellensatz over an arbitrary field. A digression on Euclidian rings is followed by a thorough study of the arithmetic theory of cubic surfaces. Subsequent chapters are devoted to p-adic fields, the Hasse principle, and the subtle notion of Diophantine dimension of fields. All chapters contain exercises, with hints or complete solutions. Notes on Geometry and Arithmetic will appeal to a wide readership, ranging from graduate students through to researchers. Assuming only a basic background in abstract algebra and number theory, the text uses Diophantine questions to motivate readers seeking an accessible pathway into arithmetic geometry.
Author : Sir Thomas L. Heath
Publisher : Heath Press
Page : 408 pages
File Size : 48,6 Mb
Release : 2008-11
Category : History
ISBN : 9781443730235
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1902 Excerpt: ...earth. r' = radius of moon, or other body. P = moon's horizontal parallax = earth's angular semidiameter as seen from the moon. f = moon's angular semidiameter. Now = P (in circular measure), r'-r = r (in circular measure);.'. r: r':: P: P', or (radius of earth): (radios of moon):: (moon's parallax): (moon's semidiameter). Examples. 1. Taking the moon's horizontal parallax as 57', and its angular diameter as 32', find its radius in miles, assuming the earth's radius to be 4000 miles. Here moon's semidiameter = 16';.-. 4000::: 57': 16';.-. r = 400 16 = 1123 miles. 2. The sun's horizontal parallax being 8"8, and his angular diameter 32V find his diameter in miles. ' Am. 872,727 miles. 3. The synodic period of Venus being 584 days, find the angle gained in each minute of time on the earth round the sun as centre. Am. l"-54 per minute. 4. Find the angular velocity with which Venus crosses the sun's disc, assuming the distances of Venus and the earth from the sun are as 7 to 10, as given by Bode's Law. Since (fig. 50) S V: VA:: 7: 3. But Srhas a relative angular velocity round the sun of l"-54 per minute (see Example 3); therefore, the relative angular velocity of A V round A is greater than this in the ratio of 7: 3, which gives an approximate result of 3"-6 per minute, the true rate being about 4" per minute. Annual ParaUax. 95. We have already seen that no displacement of the observer due to a change of position on the earth's surface could apparently affect the direction of a fixed star. However, as the earth in its annual motion describes an orbit of about 92 million miles radius round the sun, the different positions in space from which an observer views the fixed stars from time to time throughout the year must be separated ...
Author : Serafina Cuomo
Publisher : Routledge
Page : 519 pages
File Size : 47,9 Mb
Release : 2005-08-19
Category : History
ISBN : 9781134710188
The theorem of Pythagoras, Euclid's "Elements", Archimedes' method to find the volume of a sphere: all parts of the invaluable legacy of ancient mathematics. But ancient mathematics was also about counting and measuring, surveying land and attributing mystical significance to the number six. This volume offers the first accessible survey of the discipline in all its variety and diversity of practices. The period covered ranges from the fifth century BC to the sixth century AD, with the focus on the Mediterranean region. Topics include: * mathematics and politics in classical Greece * the formation of mathematical traditions * the self-image of mathematicians in the Graeco-Roman period * mathematics and Christianity * and the use of the mathematical past in late antiquity.
Author : Judith Herrin
Publisher : Princeton University Press
Page : 390 pages
File Size : 42,6 Mb
Release : 2013-03-18
Category : History
ISBN : 9781400845224
This volume explores the political, cultural, and ecclesiastical forces that linked the metropolis of Byzantium to the margins of its far-flung empire. Focusing on the provincial region of Hellas and Peloponnesos in central and southern Greece, Judith Herrin shows how the prestige of Constantinople was reflected in the military, civilian, and ecclesiastical officials sent out to govern the provinces. She evokes the ideology and culture of the center by examining different aspects of the imperial court, including diplomacy, ceremony, intellectual life, and relations with the church. Particular topics treat the transmission of mathematical manuscripts, the burning of offensive material, and the church's role in distributing philanthropy. Herrin contrasts life in the capital with provincial life, tracing the adaptation of a largely rural population to rule by Constantinople from the early medieval period onward. The letters of Michael Choniates, archbishop of Athens from 1182 to 1205, offer a detailed account of how this highly educated cleric coped with life in an imperial backwater, and demonstrate a synthesis of ancient Greek culture and medieval Christianity that was characteristic of the Byzantine elite. This collection of essays spans the entirety of Herrin's influential career and draws together a significant body of scholarship on problems of empire. It features a general introduction, two previously unpublished essays, and a concise introduction to each essay that describes how it came to be written and how it fits into her broader analysis of the unusual brilliance and longevity of Byzantium.
Author : Sir Thomas Little Heath
Publisher : Unknown
Page : 387 pages
File Size : 53,5 Mb
Release : 1978
Category : Algebra
ISBN : OCLC:220672272
Author : Marlow Anderson,Victor Katz,Robin Wilson
Publisher : American Mathematical Society
Page : 399 pages
File Size : 44,6 Mb
Release : 2022-04-26
Category : Mathematics
ISBN : 9781470470036
Covering a span of almost 4000 years, from the ancient Babylonians to the eighteenth century, this collection chronicles the enormous changes in mathematical thinking over this time as viewed by distinguished historians of mathematics from the past and the present. Each of the four sections of the book (Ancient Mathematics, Medieval and Renaissance Mathematics, The Seventeenth Century, The Eighteenth Century) is preceded by a Foreword, in which the articles are put into historical context, and followed by an Afterword, in which they are reviewed in the light of current historical scholarship. In more than one case, two articles on the same topic are included to show how knowledge and views about the topic changed over the years. This book will be enjoyed by anyone interested in mathematics and its history - and, in particular, by mathematics teachers at secondary, college, and university levels.
Author : Leonhard Euler
Publisher : Unknown
Page : 960 pages
File Size : 40,9 Mb
Release : 1810
Category : Algebra
ISBN : IOWA:31858049934619
Author : THOMAS L. HEATH
Publisher : Unknown
Page : 0 pages
File Size : 54,5 Mb
Release : 2018
Category : Electronic
ISBN : 1033142999
Author : Sir Thomas Little Heath,Leonhard Euler
Publisher : Unknown
Page : 387 pages
File Size : 48,7 Mb
Release : 1910
Category : Fermat's theorem
ISBN : 9781440064388
Author : Rebecca Buxton,Lisa Whiting
Publisher : Unbound Publishing
Page : 203 pages
File Size : 45,6 Mb
Release : 2020-09-17
Category : Philosophy
ISBN : 9781783528295
'This is brilliant. A book about women in philosophy by women in philosophy – love it!' Elif Shafak Where are the women philosophers? The answer is right here. The history of philosophy has not done women justice: you’ve probably heard the names Plato, Kant, Nietzsche and Locke – but what about Hypatia, Arendt, Oluwole and Young? The Philosopher Queens is a long-awaited book about the lives and works of women in philosophy by women in philosophy. This collection brings to centre stage twenty prominent women whose ideas have had a profound – but for the most part uncredited – impact on the world. You’ll learn about Ban Zhao, the first woman historian in ancient Chinese history; Angela Davis, perhaps the most iconic symbol of the American Black Power Movement; Azizah Y. al-Hibri, known for examining the intersection of Islamic law and gender equality; and many more. For anyone who has wondered where the women philosophers are, or anyone curious about the history of ideas – it's time to meet the philosopher queens.
Author : Sir Thomas Little Health
Publisher : Unknown
Page : 302 pages
File Size : 50,6 Mb
Release : 1885
Category : Fermat's theorem
ISBN : IOWA:31858025836085
