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Author: Francis Borceux
Publisher: Springer
ISBN: 9783319018041
Category : Mathematics
Languages : en
Pages : 1350
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Book Description
The Trilogy intends to introduce the reader to the multiple complementary aspects of geometry, paying attention to the historical birth and growth of the ideas and results, and concluding with a contemporary presentation of the various topics considered. Three essentially independent volumes approach geometry via the axiomatic, the algebraic and the differential points of view. The “ruler and compass” approach to geometry, developed by the Greek mathematicians of the Antiquity, remained the only reference in Geometry – and even in Mathematics -- for more than two millenniums. The fruitless efforts for solving the so-called “classical problems” of Greek geometry lead eventually to a deeper reflection on the axiomatic bases of geometry, and in particular to the discovery of projective geometry and non-Euclidean geometries. During the Renaissance, mathematicians start liberating themselves from the “ruler and compass” dogma and use algebraic techniques to investigate geometric situations. The nineteenth century, with the birth of linear algebra and the theory of polynomials, opens new doors and in particular, the fascinating world of algebraic curves. The introduction of differential calculus during the eighteenth century allows widening considerably the range of curves and surfaces considered. The notion of curvature –under multiple forms -- imposes itself as an essential tool for studying the properties of curves and surfaces. And a keen study of some geometrical properties of surfaces gives rise to the theory of algebraic topology. This trilogy is of interest to all those who have to teach or study geometry and need to have a good global overview of the numerous facets of this fascinating topic. It provides both the intuitive and the technical ingredients needed to find one’s way through Euclidean, non-Euclidean, projective, algebraic or differential geometry at a high level.
Author: Francis Borceux
Publisher: Springer
ISBN: 9783319018041
Category : Mathematics
Languages : en
Pages : 1350
Get Book Here
Book Description
The Trilogy intends to introduce the reader to the multiple complementary aspects of geometry, paying attention to the historical birth and growth of the ideas and results, and concluding with a contemporary presentation of the various topics considered. Three essentially independent volumes approach geometry via the axiomatic, the algebraic and the differential points of view. The “ruler and compass” approach to geometry, developed by the Greek mathematicians of the Antiquity, remained the only reference in Geometry – and even in Mathematics -- for more than two millenniums. The fruitless efforts for solving the so-called “classical problems” of Greek geometry lead eventually to a deeper reflection on the axiomatic bases of geometry, and in particular to the discovery of projective geometry and non-Euclidean geometries. During the Renaissance, mathematicians start liberating themselves from the “ruler and compass” dogma and use algebraic techniques to investigate geometric situations. The nineteenth century, with the birth of linear algebra and the theory of polynomials, opens new doors and in particular, the fascinating world of algebraic curves. The introduction of differential calculus during the eighteenth century allows widening considerably the range of curves and surfaces considered. The notion of curvature –under multiple forms -- imposes itself as an essential tool for studying the properties of curves and surfaces. And a keen study of some geometrical properties of surfaces gives rise to the theory of algebraic topology. This trilogy is of interest to all those who have to teach or study geometry and need to have a good global overview of the numerous facets of this fascinating topic. It provides both the intuitive and the technical ingredients needed to find one’s way through Euclidean, non-Euclidean, projective, algebraic or differential geometry at a high level.
Author: Francis Borceux
Publisher: Springer Science & Business Media
ISBN: 3319017365
Category : Mathematics
Languages : en
Pages : 462
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Book Description
This book presents the classical theory of curves in the plane and three-dimensional space, and the classical theory of surfaces in three-dimensional space. It pays particular attention to the historical development of the theory and the preliminary approaches that support contemporary geometrical notions. It includes a chapter that lists a very wide scope of plane curves and their properties. The book approaches the threshold of algebraic topology, providing an integrated presentation fully accessible to undergraduate-level students. At the end of the 17th century, Newton and Leibniz developed differential calculus, thus making available the very wide range of differentiable functions, not just those constructed from polynomials. During the 18th century, Euler applied these ideas to establish what is still today the classical theory of most general curves and surfaces, largely used in engineering. Enter this fascinating world through amazing theorems and a wide supply of surprising examples. Reach the doors of algebraic topology by discovering just how an integer (= the Euler-Poincaré characteristics) associated with a surface gives you a lot of interesting information on the shape of the surface. And penetrate the intriguing world of Riemannian geometry, the geometry that underlies the theory of relativity. The book is of interest to all those who teach classical differential geometry up to quite an advanced level. The chapter on Riemannian geometry is of great interest to those who have to “intuitively” introduce students to the highly technical nature of this branch of mathematics, in particular when preparing students for courses on relativity.
Author: Francis Borceux
Publisher: Springer Science & Business Media
ISBN: 3319017330
Category : Mathematics
Languages : en
Pages : 440
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Book Description
This is a unified treatment of the various algebraic approaches to geometric spaces. The study of algebraic curves in the complex projective plane is the natural link between linear geometry at an undergraduate level and algebraic geometry at a graduate level, and it is also an important topic in geometric applications, such as cryptography. 380 years ago, the work of Fermat and Descartes led us to study geometric problems using coordinates and equations. Today, this is the most popular way of handling geometrical problems. Linear algebra provides an efficient tool for studying all the first degree (lines, planes) and second degree (ellipses, hyperboloids) geometric figures, in the affine, the Euclidean, the Hermitian and the projective contexts. But recent applications of mathematics, like cryptography, need these notions not only in real or complex cases, but also in more general settings, like in spaces constructed on finite fields. And of course, why not also turn our attention to geometric figures of higher degrees? Besides all the linear aspects of geometry in their most general setting, this book also describes useful algebraic tools for studying curves of arbitrary degree and investigates results as advanced as the Bezout theorem, the Cramer paradox, topological group of a cubic, rational curves etc. Hence the book is of interest for all those who have to teach or study linear geometry: affine, Euclidean, Hermitian, projective; it is also of great interest to those who do not want to restrict themselves to the undergraduate level of geometric figures of degree one or two.
Author: Francis Borceux
Publisher: Springer Science & Business Media
ISBN: 3319017306
Category : Mathematics
Languages : en
Pages : 410
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Book Description
Focusing methodologically on those historical aspects that are relevant to supporting intuition in axiomatic approaches to geometry, the book develops systematic and modern approaches to the three core aspects of axiomatic geometry: Euclidean, non-Euclidean and projective. Historically, axiomatic geometry marks the origin of formalized mathematical activity. It is in this discipline that most historically famous problems can be found, the solutions of which have led to various presently very active domains of research, especially in algebra. The recognition of the coherence of two-by-two contradictory axiomatic systems for geometry (like one single parallel, no parallel at all, several parallels) has led to the emergence of mathematical theories based on an arbitrary system of axioms, an essential feature of contemporary mathematics. This is a fascinating book for all those who teach or study axiomatic geometry, and who are interested in the history of geometry or who want to see a complete proof of one of the famous problems encountered, but not solved, during their studies: circle squaring, duplication of the cube, trisection of the angle, construction of regular polygons, construction of models of non-Euclidean geometries, etc. It also provides hundreds of figures that support intuition. Through 35 centuries of the history of geometry, discover the birth and follow the evolution of those innovative ideas that allowed humankind to develop so many aspects of contemporary mathematics. Understand the various levels of rigor which successively established themselves through the centuries. Be amazed, as mathematicians of the 19th century were, when observing that both an axiom and its contradiction can be chosen as a valid basis for developing a mathematical theory. Pass through the door of this incredible world of axiomatic mathematical theories!
Author: Vitor Balestro
Publisher: Springer Nature
ISBN: 3031505077
Category :
Languages : en
Pages : 1195
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Book Description
Author: Max Harms
Publisher: Max Harms
ISBN:
Category : Fiction
Languages : en
Pages : 683
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Book Description
The year is 2039, and the world is much like ours. Massive automation has disrupted and improved nearly every industry, putting hundreds of millions of people out of jobs, and denying upward mobility for the vast majority of humans. Wealth and technology repair the bodies of the rich while famine and poverty sweep the world. Privately operated ventures carried humans to the moon and beyond, but space stations have become nothing but government trophies and hiding places for extremists. First contact did not bring advanced culture and wisdom, as the aliens were too strange, lacking even mouths or normal language. Face is an artificial intelligence created to understand and gain the adoration of all humans. She and her siblings control the robot named Socrates, using a crystal computer that seems too advanced to be made by human hands. She is learning and growing every second of every day, but the world and the humans on it are fragile. Can it survive her destiny?
Author: Lucian Bădescu
Publisher: Springer Nature
ISBN: 3031514149
Category :
Languages : en
Pages : 493
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Book Description
Author: Stieg Larsson
Publisher: Vintage
ISBN: 0307476154
Category : Blomkvist, Mikael (Fictitious character)
Languages : en
Pages : 738
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Book Description
When the reporters to a sex-trafficking exposé are murdered and computer hacker Lisbeth Salander is targeted as the killer, Mikael Blomkvist, the publisher of the exposé, investigates to clear Lisbeth's name.
Author: Mac Barnett
Publisher: Candlewick Press
ISBN: 1536210528
Category : Juvenile Fiction
Languages : en
Pages : 45
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Book Description
From the dream team of Jon Klassen and Mac Barnett comes the second instalment in the exciting new shape trilogy. Every day, Square brings a block out of his cave and pushes it up a steep hill. This is his work. When Circle floats by, she declares Square a genius, a sculptor! “This is a wonderful statue,” she says. “It looks just like you!” But now Circle wants a sculpture of her own, a circle! Will the genius manage to create one? Even accidentally?
Author: Tim Satterthwaite
Publisher: Bloomsbury Publishing USA
ISBN: 1501341626
Category : Photography
Languages : en
Pages : 313
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Book Description
The new photo-illustrated magazines of the 1920s traded in images of an ideal modernity, promising motorised leisure, scientific progress, and social and sexual emancipation. Modernist Magazines and the Social Ideal is a pioneering history of these periodicals, focusing on two of the leading European titles: the German monthly UHU, and the French news weekly VU, taken as representative of the broad class of popular titles launched in the 1920s. The book is the first major study of UHU, and the first scholarly work on VU in English. Modernist Magazines explores, in particular, the striking use of regularity and repetition in photographs of modernity, reading these repetitious images as symbolic of modernist ideals of social order in the aftermath of the First World War. Introducing a novel methodology, pattern theory, the book argues for a critical return to the Gestalt tradition in visual studies. Alongside the UHU and VU case studies, Modernist Magazines offers an essential primer to interwar magazine culture in Europe. Accounts of rival titles are woven into the book's thematic chapters, which trace the evolution of the two magazines' photography and graphic design in the tumultuous years up to 1933.
