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| diophantus images: Experimental Photogrammetry of Lunar Images Sherman S. C. Wu, Henry J. Moore, 1980 An experimental photogrammetric study, using Appolo orbital photographs for geologic studies of the Moon and the exploration of the Moon and other planetary bodies. |
| diophantus images: Diophantus and Diophantine Equations Isabella Grigoryevna Bashmakova, 2019-01-18 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 Renaissance and in the work of Fermat. This account is continued to our own day and ends with an afterword by Joseph Silverman, who notes the most recent developments including the proof of Fermat's Last Theorem. |
| diophantus images: The Arithmetica of Diophantus Jean Christianidis, Jeffrey Oaks, 2022-11-01 This volume offers an English translation of all ten extant books of Diophantus of Alexandria’s Arithmetica, along with a comprehensive conceptual, historical, and mathematical commentary. Before his work became the inspiration for the emerging field of number theory in the seventeenth century, Diophantus (ca. 3rd c. CE) was known primarily as an algebraist. This volume explains how his method of solving arithmetical problems agrees both conceptually and procedurally with the premodern algebra later practiced in Arabic, Latin, and European vernaculars, and how this algebra differs radically from the modern algebra initiated by François Viète and René Descartes. It also discusses other surviving traces of ancient Greek algebra and follows the influence of the Arithmetica in medieval Islam, Byzantium, and the European Renaissance down to the 1621 publication of Claude-Gaspard Bachet’s edition. After the English translation the book provides a problem-by-problem commentary explaining the solutions in a manner compatible with Diophantus’s mode of thought. The Arithmetica of Diophantus provides an invaluable resource for historians of mathematics, science, and technology, as well as those studying ancient Greek, medieval Islamic and Byzantine, and Renaissance history. In addition, the volume is also suitable for mathematicians and mathematics educators. |
| diophantus images: Combinatorial Image Analysis Reinhard Klette, Jovisa Zunic, 2004-11-03 This volume presents the proceedings of the 10th International Workshop on Combinatorial Image Analysis, held December 1–3, 2004, in Auckland, New Zealand. Prior meetings took place in Paris (France, 1991), Ube (Japan, 1992), Washington DC (USA, 1994), Lyon (France, 1995), Hiroshima (Japan, 1997), Madras (India, 1999), Caen (France, 2000), Philadelphia (USA, 2001), and - lermo (Italy, 2003). For this workshop we received 86 submitted papers from 23 countries. Each paper was evaluated by at least two independent referees. We selected 55 papers for the conference. Three invited lectures by Vladimir Kovalevsky (Berlin), Akira Nakamura (Hiroshima), and Maurice Nivat (Paris) completed the program. Conference papers are presented in this volume under the following topical part titles: discrete tomography (3 papers), combinatorics and computational models (6), combinatorial algorithms (6), combinatorial mathematics (4), d- ital topology (7), digital geometry (7), approximation of digital sets by curves and surfaces (5), algebraic approaches (5), fuzzy image analysis (2), image s- mentation (6), and matching and recognition (7). These subjects are dealt with in the context of digital image analysis or computer vision. |
| diophantus images: Advanced Image Processing Techniques and Applications Kumar, N. Suresh, Sangaiah, Arun Kumar, Arun, M., Anand, S., 2017-02-10 Today, the scope of image processing and recognition has broadened due to the gap in scientific visualization. Thus, new imaging techniques have developed, and it is imperative to study this progression for optimal utilization. Advanced Image Processing Techniques and Applications is an essential reference publication for the latest research on digital image processing advancements. Featuring expansive coverage on a broad range of topics and perspectives, such as image and video steganography, pattern recognition, and artificial vision, this publication is ideally designed for scientists, professionals, researchers, and academicians seeking current research on solutions for new challenges in image processing. |
| diophantus images: God Created The Integers Stephen Hawking, 2007-03-29 Bestselling author and physicist Stephen Hawking explores the masterpieces of mathematics, 25 landmarks spanning 2,500 years and representing the work of 15 mathematicians, including Augustin Cauchy, Bernard Riemann, and Alan Turing. This extensive anthology allows readers to peer into the mind of genius by providing them with excerpts from the original mathematical proofs and results. It also helps them understand the progression of mathematical thought, and the very foundations of our present-day technologies. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication. |
| diophantus images: Archimedes' Stomach...and Other Puzzles You'll Love To Digest Yossi Elran, 2025-04-14 Embark on a delightful sequel to Lewis Carroll's Cats and Rats ... and Other Puzzles with Interesting Tails with this new treasure trove of mathematical curiosities! Like its predecessor, this book is a homage to recreational mathematics, inspired by the ingenious works of Martin Gardner, Ian Stewart, Raymond Smullyan, and more contemporary minds like Jason Rosenhouse, Ben Orlin and Matt Parker.Each chapter unveils a new puzzle, setting the stage for a journey through mathematical thought. This book doesn't just rehash old puzzles; it breathes new life into them. From unravelling the complexities of Archimedes' Ostomachion to deciphering the intricacies of modern cryptography, the topics are as varied as they are fascinating. Dive into the relationship between mathematics and linguistics, see the solutions to ancient number puzzles in modern math art, and solve mazes with logic and intuition.Whether you're a seasoned mathematician, a curious historian, an eager student, or a teacher looking for captivating educational tools, this book is your gateway to enhancing creative thinking and innovation through the playful side of math. Prepare to be challenged, intrigued, and inspired as every page turns mathematics into an exhilarating adventure! |
| diophantus images: Diophantus and Diophantine Equations Isabella Grigoryevna Bashmakova, 2019-01-29 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. |
| diophantus images: Exploring the Number Jungle: A Journey into Diophantine Analysis Edward B. Burger, 2000 The minimal background requirements and the author's fresh approach make this book enjoyable and accessible to a wide range of students, mathematicians, and fans of number theory.--BOOK JACKET. |
| diophantus images: Handbook of the History and Philosophy of Mathematical Practice Bharath Sriraman, 2024-04-26 The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques |
| diophantus images: Revolutions and Continuity in Greek Mathematics Michalis Sialaros, 2018-04-23 This volume brings together a number of leading scholars working in the field of ancient Greek mathematics to present their latest research. In their respective area of specialization, all contributors offer stimulating approaches to questions of historical and historiographical ‘revolutions’ and ‘continuity’. Taken together, they provide a powerful lens for evaluating the applicability of Thomas Kuhn’s ideas on ‘scientific revolutions’ to the discipline of ancient Greek mathematics. Besides the latest historiographical studies on ‘geometrical algebra’ and ‘premodern algebra’, the reader will find here some papers which offer new insights into the controversial relationship between Greek and pre-Hellenic mathematical practices. Some other contributions place emphasis on the other edge of the historical spectrum, by exploring historical lines of ‘continuity’ between ancient Greek, Byzantine and post-Hellenic mathematics. The terminology employed by Greek mathematicians, along with various non-textual and material elements, is another topic which some of the essays in the volume explore. Finally, the last three articles focus on a traditionally rich source on ancient Greek mathematics; namely the works of Plato and Aristotle. |
| diophantus images: Mathematical Foundations of Image Processing and Analysis, Volume 1 Jean-Charles Pinoli, 2014-07-09 Image processing and image analysis are typically important fields in information science and technology. By “image processing”, we generally understand all kinds of operation performed on images (or sequences of images) in order to increase their quality, restore their original content, emphasize some particular aspect of the information or optimize their transmission, or to perform radiometric and/or spatial analysis. By “image analysis” we understand, however, all kinds of operation performed on images (or sequences of images) in order to extract qualitative or quantitative data, perform measurements and apply statistical analysis. Whereas there are nowadays many books dealing with image processing, only a small number deal with image analysis. The methods and techniques involved in these fields of course have a wide range of applications in our daily world: industrial vision, material imaging, medical imaging, biological imaging, multimedia applications, satellite imaging, quality control, traffic control, and so on |
| diophantus images: Encyclopedia of Image Processing Phillip A. Laplante, 2018-11-08 The Encyclopedia of Image Processing presents a vast collection of well-written articles covering image processing fundamentals (e.g. color theory, fuzzy sets, cryptography) and applications (e.g. geographic information systems, traffic analysis, forgery detection). Image processing advances have enabled many applications in healthcare, avionics, robotics, natural resource discovery, and defense, which makes this text a key asset for both academic and industrial libraries and applied scientists and engineers working in any field that utilizes image processing. Written by experts from both academia and industry, it is structured using the ACM Computing Classification System (CCS) first published in 1988, but most recently updated in 2012. |
| diophantus images: Mathematics for the IB MYP 3 Irina Amlin, Rita Bateson, 2018-08-28 A concept-driven and assessment-focused approach to Mathematics teaching and learning. - Approaches each chapter with statements of inquiry framed by key and related concepts, set in a global context - Supports every aspect of assessment using tasks designed by an experienced MYP educator - Differentiates and extends learning with research projects and interdisciplinary opportunities - Applies global contexts in meaningful ways to offer an MYP Mathematics programme with an internationally-minded perspective |
| diophantus images: Wealth, Aristocracy And Royal Propaganda Under the Hellenistic Kingdom of the Mithradatids in the Central Black Sea Region of Turkey Deniz Burcu Erciyas, 2006 This study of the reign of Mithradates VI (120-63 BC), attempts to combine the history of the belligerent Roman Empire and the indomitable kingdom of Pontus with the archaeology of the Turkish Black Sea region. |
| diophantus images: How to Guard an Art Gallery T.S. Michael, 2009-09-01 An “accessible and engaging” tool for understanding the branch of mathematics that is so crucial to modern computer science, using real-life problems (Mathematical Reviews). What is the maximum number of pizza slices one can get by making four straight cuts through a circular pizza? How does a computer determine the best set of pixels to represent a straight line on a computer screen? How many people at a minimum does it take to guard an art gallery? Discrete mathematics has the answer to these—and many other—questions of picking, choosing, and shuffling. T. S. Michael’s gem of a book brings this vital but tough-to-teach subject to life using examples from the real world and popular culture. Each chapter uses one problem—such as slicing a pizza—to detail key concepts about counting numbers and arranging finite sets. Michael takes a different perspective in tackling each of eight problems and explains them in differing degrees of generality, showing in the process how the same mathematical concepts appear in varied guises and contexts. In doing so, he imparts a broader understanding of the ideas underlying discrete mathematics and helps readers appreciate and understand mathematical thinking and discovery. This book explains the basic concepts of discrete mathematics and demonstrates how to apply them in largely nontechnical language. The explanations and formulas can be grasped with a basic understanding of linear equations. |
| diophantus images: Making up Numbers: A History of Invention in Mathematics Ekkehard Kopp, 2020-10-23 Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject. |
| diophantus images: Number Theory John J. Watkins, 2013-12-29 An introductory textbook with a unique historical approach to teaching number theory The natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they are important. This book emphasizes the historical development of number theory, describing methods, theorems, and proofs in the contexts in which they originated, and providing an accessible introduction to one of the most fascinating subjects in mathematics. Written in an informal style by an award-winning teacher, Number Theory covers prime numbers, Fibonacci numbers, and a host of other essential topics in number theory, while also telling the stories of the great mathematicians behind these developments, including Euclid, Carl Friedrich Gauss, and Sophie Germain. This one-of-a-kind introductory textbook features an extensive set of problems that enable students to actively reinforce and extend their understanding of the material, as well as fully worked solutions for many of these problems. It also includes helpful hints for when students are unsure of how to get started on a given problem. Uses a unique historical approach to teaching number theory Features numerous problems, helpful hints, and fully worked solutions Discusses fun topics like Pythagorean tuning in music, Sudoku puzzles, and arithmetic progressions of primes Includes an introduction to Sage, an easy-to-learn yet powerful open-source mathematics software package Ideal for undergraduate mathematics majors as well as non-math majors Digital solutions manual (available only to professors) |
| diophantus images: Elliptic Diophantine Equations Nikos Tzanakis, 2013-08-29 This book presents in a unified and concrete way the beautiful and deep mathematics - both theoretical and computational - on which the explicit solution of an elliptic Diophantine equation is based. It collects numerous results and methods that are scattered in the literature. Some results are hidden behind a number of routines in software packages, like Magma and Maple; professional mathematicians very often use these routines just as a black-box, having little idea about the mathematical treasure behind them. Almost 20 years have passed since the first publications on the explicit solution of elliptic Diophantine equations with the use of elliptic logarithms. The art of solving this type of equation has now reached its full maturity. The author is one of the main persons that contributed to the development of this art. The monograph presents a well-balanced combination of a variety of theoretical tools (from Diophantine geometry, algebraic number theory, theory of linear forms in logarithms of various forms - real/complex and p-adic elliptic - and classical complex analysis), clever computational methods and techniques (LLL algorithm and de Weger's reduction technique, AGM algorithm, Zagier's technique for computing elliptic integrals), ready-to-use computer packages. A result is the solution in practice of a large general class of Diophantine equations. |
| diophantus images: Drawn to Purpose Martha H. Kennedy, 2018-02-14 Winner of the 2019 Eisner Award for the Best Comics-Related Book Published in partnership with the Library of Congress, Drawn to Purpose: American Women Illustrators and Cartoonists presents an overarching survey of women in American illustration, from the late nineteenth into the twenty-first century. Martha H. Kennedy brings special attention to forms that have heretofore received scant notice—cover designs, editorial illustrations, and political cartoons—and reveals the contributions of acclaimed cartoonists and illustrators, along with many whose work has been overlooked. Featuring over 250 color illustrations, including eye-catching original art from the collections of the Library of Congress, Drawn to Purpose provides insight into the personal and professional experiences of eighty women who created these works. Included are artists Roz Chast, Lynda Barry, Lynn Johnston, and Jillian Tamaki. The artists' stories, shaped by their access to artistic training, the impact of marriage and children on careers, and experiences of gender bias in the marketplace, serve as vivid reminders of social change during a period in which the roles and interests of women broadened from the private to the public sphere. The vast, often neglected, body of artistic achievement by women remains an important part of our visual culture. The lives and work of the women responsible for it merit much further attention than they have received thus far. For readers who care about cartooning and illustration, Drawn to Purpose provides valuable insight into this rich heritage. |
| diophantus images: The Decline of the West Oswald Spengler, 2006-04-11 Since its first publication more than eighty years ago, The Decline of the West has ranked as one of the most widely read and talked about books of our time. A sweeping account of Western culture by a historian of legendary intellect, it is an astonishingly informed, forcefully eloquent, thrillingly controversial work that advances a world view based on the cyclical rise and fall of civilizations. This abridgment presents the most significant of Oswald Spengler’s arguments, linked by illuminating explanatory passages. It makes available in one volume a masterpiece of grand-scale history and far-reaching prophesy that remains essential reading for anyone interested in the factors that determine the course of civilizations. |
| diophantus images: Multidimensional Discrete Unitary Transforms Artyom M. Grigoryan, Sos S. Agaian, 2003-07-31 This reference presents a more efficient, flexible, and manageable approach to unitary transform calculation and examines novel concepts in the design, classification, and management of fast algorithms for different transforms in one-, two-, and multidimensional cases. Illustrating methods to construct new unitary transforms for best algorithm selection and development in real-world applications, the book contains a wide range of examples to compare the efficacy of different algorithms in a variety of one-, two-, and three-dimensional cases. Multidimensional Discrete Unitary Transforms builds progressively from simple representative cases to higher levels of generalization. |
| diophantus images: The New Yearbook for Phenomenology and Phenomenological Philosophy Burt Hopkins, John Drummond, 2021-09-20 Volume XVIII Special Issue: Gian-Carlo Rota and The End of Objectivity, 2019 Aim and Scope: The New Yearbook for Phenomenology and Phenomenological Philosophy provides an annual international forum for phenomenological research in the spirit of Husserl's groundbreaking work and the extension of this work by such figures as Scheler, Heidegger, Sartre, Levinas, Merleau-Ponty and Gadamer. Contributors: Gabriele Baratelli, Stefania Centrone, Giovanna C. Cifoletti, Jean-Marie Coquard, Steven Crowell, Deborah De Rosa, Daniele De Santis, Nicolas de Warren, Agnese Di Riccio, Aurélien Djian, Yuval Dolev, Mirja Hartimo, Burt C. Hopkins, Talia Leven, Ah Hyun Moon, Luis Niel, Fabrizio Palombi, Mario Ariel González Porta, Gian-Carlo Rota, Michael Roubach, Franco Trabattoni and Michele Vagnetti. Submissions: Manuscripts, prepared for blind review, should be submitted to the Editors (burt-crowell.hopkins@univ-lille3.fr and drummond@fordham.edu) electronically via e-mail attachments. |
| diophantus images: The Way of Being Edward P. Butler, 2023-08-19 The success of Western powers in the Modern era has enabled the Western civilizational perspective and its self-understanding to present itself to the rest of the world, not as one perspective among others, but as the universal and definitive human perspective and as the culmination of the world’s intellectual and spiritual development according to principles supposedly objective and self-evident. The hegemony of this civilizational perspective makes it imperative that the basic elements of the Western paradigm of thought referenced by Western geopolitical power as the source of its legitimacy be grasped and critiqued. This book, using as its basis a relatively standard sequence of works seen as comprising the ‘Western Canon’, seeks to provide the foundation for such awareness, both to appreciate the wisdom in this intensely contested tradition as well as recognizing its hazards. |
| diophantus images: Calculus in Context Alexander Hahn, 2017-04-15 A new approach to teaching calculus that uses historical examples and draws on applications from science and engineering. Breaking the mold of existing calculus textbooks, Calculus in Context draws students into the subject in two new ways. Part I develops the mathematical preliminaries (including geometry, trigonometry, algebra, and coordinate geometry) within the historical frame of the ancient Greeks and the heliocentric revolution in astronomy. Part II starts with comprehensive and modern treatments of the fundamentals of both differential and integral calculus, then turns to a wide-ranging discussion of applications. Students will learn that core ideas of calculus are central to concepts such as acceleration, force, momentum, torque, inertia, and the properties of lenses. Classroom-tested at Notre Dame University, this textbook is suitable for students of wide-ranging backgrounds because it engages its subject at several levels and offers ample and flexible problem set options for instructors. Parts I and II are both supplemented by expansive Problems and Projects segments. Topics covered in the book include: • the basics of geometry, trigonometry, algebra, and coordinate geometry and the historical, scientific agenda that drove their development • a brief, introductory calculus from the works of Newton and Leibniz • a modern development of the essentials of differential and integral calculus • the analysis of specific, relatable applications, such as the arc of the George Washington Bridge; the dome of the Pantheon; the optics of a telescope; the dynamics of a bullet; the geometry of the pseudosphere; the motion of a planet in orbit; and the momentum of an object in free fall. Calculus in Context is a compelling exploration—for students and instructors alike—of a discipline that is both rich in conceptual beauty and broad in its applied relevance. |
| diophantus images: The Role of the History of Mathematics in the Teaching/Learning Process Sixto Romero Sanchez, Ana Serradó Bayés, Peter Appelbaum, Gilles Aldon, 2023-06-15 This volume presents multiple perspectives on the uses of the history of mathematics for teaching and learning, including the value of historical topics in challenging mathematics tasks, for provoking teachers’ reflection on the nature of mathematics, curriculum development questions that mirror earlier pedagogical choices in the history of mathematics education, and the history of technological innovations in the teaching and learning of mathematics. An ethnomathematical perspective on the history of mathematics challenges readers to appreciate the role of mathematics in perpetuating consequences of colonialism. Histories of the textbook and its uses offer interesting insights into how technology has changed the fundamental role of curriculum materials and classroom pedagogies. History is explored as a source for the training of teachers, for good puzzles and problems, and for a broad understanding of mathematics education policy. Third in a series of sourcebooks from the International Commission for the Study and Improvement of Mathematics Teaching, this collection of cutting-edge research, stories from the field, and policy implications is a contemporary and global perspective on current possibilities for the history of mathematics for mathematics education. This latest volume integrates discussions regarding history of mathematics, history of mathematics education and history of technology for education that have taken place at the Commission's recent annual conferences. |
| diophantus images: Commentaries and Annotations on the Holy Scriptures,. John HEWLETT (B.D.), 1816 |
| diophantus images: Commentaries and Annotations on the Holy Scriptures John Hewlett, 1816 |
| diophantus images: Diophantus of Alexandria Thomas L. Heath, 1910 |
| diophantus images: Geological Survey Professional Paper Geological Survey (U.S.), 1980 |
| diophantus images: An Introduction to the Symbolic Literature of the Renaissance , |
| diophantus images: Beautiful Mathematics Martin Erickson, 2011-12-22 Mathematical ideas with aesthetic appeal for any mathematically minded person. |
| diophantus images: Enlightening Symbols Joseph Mazur, 2016-12-06 An entertaining look at the origins of mathematical symbols While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today. |
| diophantus images: Alhacen on Image-formation and Distortion in Mirrors Alhazen, 2008 |
| diophantus images: Professor Higgins's Problem Collection Peter M. Higgins, 2017 This book serves up a variety of problems and shows how mathematics answers them. Topics range from cracking codes to the persistence of recessive genes. |
| diophantus images: Alhacen on image-formation and distortion in mirrors A. Mark Smith, 2008 Ch. 1; Ch. 2; Ch. 3: Analysis of Plane Mirrors: Proposition 1; Ch. 4: Analysis of Convex Spherical Mirrors: Propositions 2-15; Ch. 5: Analysis of Convex Cylindrical Mirrors: Propositions 16-19; Ch. 6: Analysis of Convex Conical Mirrors: Propositions 20-22; Ch. 7: Analysis of Concave Spherical Mirrors: Propositions 33-36; Ch. 8: Analysis of Concave Cylindrical Mirrors: Propositions 37 and 38. Figures for Translation and Commentary; Appendix; Latin-English Index; English-Latin Glossary; Bibliography; General Index. Illus. (sold with Vol. 1: -- see 1-60618-981-6 -- must buy both vol.) |
| diophantus images: U.S. Geological Survey Professional Paper , 1980 |
| diophantus images: Diophantine Analysis Robert Daniel Carmichael, 1915 |
| diophantus images: Sourcebook in the Mathematics of Ancient Greece and the Eastern Mediterranean Victor J. Katz, 2024-09-17 In recent decades, there has been extensive research on Greek mathematics that has considerably enlarged the scope of this area of inquiry. Traditionally, Greek mathematics has referred to the axiomatic work of Archimedes, Apollonius, and others in the first three centuries BCE. However, there is a wide body of mathematical work that appeared in the eastern Mediterranean during the time it was under Greek influence (from approximately 400 BCE to 600 CE), which remains under-explored in the existing scholarship. This sourcebook provides an updated look at Greek mathematics, bringing together classic Greek texts with material from lesser-known authors, as well as newly uncovered texts that have been omitted in previous scholarship. The book adopts a broad scope in defining mathematical practice, and as such, includes fields such as music, optics, and architecture. It includes important sources written in languages other than Greek in the eastern Mediterranean area during the period from 400 BCE to 600 CE, which show some influence from Greek culture. It also includes passages that highlight the important role mathematics played in philosophy, pedagogy, and popular culture. The book is organized topically; chapters include arithmetic, plane geometry, astronomy, and philosophy, literature, and education. Within each chapter, the (translated) texts are organized chronologically. The book weaves together ancient commentary on classic Greek works with the works themselves to show how the understanding of mathematical ideas changed over the centuries-- |
| diophantus images: Algorithmic and Combinatorial Algebra L.A. Bokut', G.P.. Kukin, 2012-12-06 Even three decades ago, the words 'combinatorial algebra' contrasting, for in stance, the words 'combinatorial topology,' were not a common designation for some branch of mathematics. The collocation 'combinatorial group theory' seems to ap pear first as the title of the book by A. Karras, W. Magnus, and D. Solitar [182] and, later on, it served as the title of the book by R. C. Lyndon and P. Schupp [247]. Nowadays, specialists do not question the existence of 'combinatorial algebra' as a special algebraic activity. The activity is distinguished not only by its objects of research (that are effectively given to some extent) but also by its methods (ef fective to some extent). To be more exact, we could approximately define the term 'combinatorial algebra' for the purposes of this book, as follows: So we call a part of algebra dealing with groups, semi groups , associative algebras, Lie algebras, and other algebraic systems which are given by generators and defining relations {in the first and particular place, free groups, semigroups, algebras, etc. )j a part in which we study universal constructions, viz. free products, lINN-extensions, etc. j and, finally, a part where specific methods such as the Composition Method (in other words, the Diamond Lemma, see [49]) are applied. Surely, the above explanation is far from covering the full scope of the term (compare the prefaces to the books mentioned above). |
Diophantus' Lifespan - Mathematics Stack Exchange
Today I saw Diophantus' Epitaph. For those of you who don't know it and don't feel like googling: 'Here lies Diophantus,' the wonder behold. Through art algebraic, the stone tells how old: 'God...
reference request - Is there an English translation of Diophantus's ...
Aug 24, 2011 · Is Heath's book really a translation? It seems more like a book ABOUT Diophantus's "Arithmetica", not the translation of the actual book. There's just an "abstract" …
How to solve the problem that determines the age of Diophantus?
Let D D be the number of years Diophantus lived, and S S the number of years his son lived. First we make an obvious relation, that his son lived for half his own lifetime.
Are problems in "Arithmetica" of Diophantus all solved now?
Jan 31, 2019 · It's well-known that Diophantus had written ”Diophantus“ which contains many problems about solving arithmetic equations. I wonder whether all of them has been solved …
Fermat's Notes on Diophantus - Mathematics Stack Exchange
Aug 17, 2016 · I am looking for a free online copy of Diophantus' Arithmetica as well as Fermat's Notes on it. After some google searching, I couldn't find any. Thanks for your help! Edit: …
How to find solutions of linear Diophantine ax + by = c?
The diophantine equation ax + by = c has solutions if and only if gcd(a, b) c. If so, it has infinitely many solutions, and any one solution can be used to generate all the other ones. To see this, …
abstract algebra - Diophantus math - Mathematics Stack Exchange
Diophantus math Ask Question Asked 11 years, 7 months ago Modified 11 years, 7 months ago
Nonlinear system Diophantus. - Mathematics Stack Exchange
Aug 18, 2015 · In the extant books of Diophantus, are considered in the system of equations. Of interest is the non-linear system of Diophantine equations. Some simple systems from his …
Question on proving Primitive Pythagorean triples using …
Jan 25, 2020 · Question on proving Primitive Pythagorean triples using Diophantus method? [duplicate] Ask Question Asked 5 years, 4 months ago Modified 5 years, 4 months ago
abstract algebra - Diophantus mathematics - Mathematics Stack …
Find a number whose subtraction from two given numbers (say, $9$ and $21$) allows both differences to be squares. Call the required number $9 - x^2$ so that the condition holds …
Diophantus' Lifespan - Mathematics Stack Exchange
Today I saw Diophantus' Epitaph. For those of you who don't know it and don't feel like googling: 'Here lies Diophantus,' the wonder behold. Through art algebraic, the stone tells how old: 'God...
reference request - Is there an English translation of Diophantus's ...
Aug 24, 2011 · Is Heath's book really a translation? It seems more like a book ABOUT Diophantus's "Arithmetica", not the translation of the actual book. There's just an "abstract" …
How to solve the problem that determines the age of Diophantus?
Let D D be the number of years Diophantus lived, and S S the number of years his son lived. First we make an obvious relation, that his son lived for half his own lifetime.
Are problems in "Arithmetica" of Diophantus all solved now?
Jan 31, 2019 · It's well-known that Diophantus had written ”Diophantus“ which contains many problems about solving arithmetic equations. I wonder whether all of them has been solved …
Fermat's Notes on Diophantus - Mathematics Stack Exchange
Aug 17, 2016 · I am looking for a free online copy of Diophantus' Arithmetica as well as Fermat's Notes on it. After some google searching, I couldn't find any. Thanks for your help! Edit: …
How to find solutions of linear Diophantine ax + by = c?
The diophantine equation ax + by = c has solutions if and only if gcd(a, b) c. If so, it has infinitely many solutions, and any one solution can be used to generate all the other ones. To see this, …
abstract algebra - Diophantus math - Mathematics Stack Exchange
Diophantus math Ask Question Asked 11 years, 7 months ago Modified 11 years, 7 months ago
Nonlinear system Diophantus. - Mathematics Stack Exchange
Aug 18, 2015 · In the extant books of Diophantus, are considered in the system of equations. Of interest is the non-linear system of Diophantine equations. Some simple systems from his …
Question on proving Primitive Pythagorean triples using …
Jan 25, 2020 · Question on proving Primitive Pythagorean triples using Diophantus method? [duplicate] Ask Question Asked 5 years, 4 months ago Modified 5 years, 4 months ago
abstract algebra - Diophantus mathematics - Mathematics Stack …
Find a number whose subtraction from two given numbers (say, $9$ and $21$) allows both differences to be squares. Call the required number $9 - x^2$ so that the condition holds …
