Conics And Cubics

Author : Robert Bix
Publisher : Springer Science & Business Media
ISBN 13 : 1475729758
Total Pages : 300 pages
Book Rating : 4.57/5 ( download)

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Download or read book Conics and Cubics written by Robert Bix and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic curves are the graphs of polynomial equations in two vari 3 ables, such as y3 + 5xy2 = x + 2xy. By focusing on curves of degree at most 3-lines, conics, and cubics-this book aims to fill the gap between the familiar subject of analytic geometry and the general study of alge braic curves. This text is designed for a one-semester class that serves both as a a geometry course for mathematics majors in general and as a sequel to college geometry for teachers of secondary school mathe matics. The only prerequisite is first-year calculus. On the one hand, this book can serve as a text for an undergraduate geometry course for all mathematics majors. Algebraic geometry unites algebra, geometry, topology, and analysis, and it is one of the most exciting areas of modem mathematics. Unfortunately, the subject is not easily accessible, and most introductory courses require a prohibitive amount of mathematical machinery. We avoid this problem by focusing on curves of degree at most 3. This keeps the results tangible and the proofs natural. It lets us emphasize the power of two fundamental ideas, homogeneous coordinates and intersection multiplicities.

Author : Robert Bix
Publisher : Springer
ISBN 13 : 9780387511986
Total Pages : 0 pages
Book Rating : 4.89/5 ( download)

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Download or read book Conics and Cubics written by Robert Bix and published by Springer. This book was released on 2008-11-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout’s Theorem on the number of intersections of two curves. The subject area is described by means of concrete and accessible examples. The book is a text for a one-semester course.

Author : Henry Seely White
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.16/5 ( download)

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Download or read book Triangles and Quadrilaterals Inscribed to a Cubic and Circumscribed to a Conic written by Henry Seely White and published by . This book was released on 1906 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Séverine Fiedler - Le Touzé
Publisher : CRC Press
ISBN 13 : 0429838247
Total Pages : 238 pages
Book Rating : 4.48/5 ( download)

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Download or read book Pencils of Cubics and Algebraic Curves in the Real Projective Plane written by Séverine Fiedler - Le Touzé and published by CRC Press. This book was released on 2018-12-07 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP2. Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first section in this book answers questions such as, can one count the combinatorial configurations up to the action of the symmetric group? How are they pairwise connected via almost generic configurations? These questions are addressed using rational cubics and pencils of cubics for n = 6 and 7. The book’s second section deals with configurations of eight points in the convex position. Both the combinatorial configurations and combinatorial pencils are classified up to the action of the dihedral group D8. Finally, the third section contains plentiful applications and results around Hilbert’s sixteenth problem. The author meticulously wrote this book based upon years of research devoted to the topic. The book is particularly useful for researchers and graduate students interested in topology, algebraic geometry and combinatorics. Features: Examines how the shape of pencils depends on the corresponding configurations of points Includes topology of real algebraic curves Contains numerous applications and results around Hilbert’s sixteenth problem About the Author: Séverine Fiedler-le Touzé has published several papers on this topic and has been invited to present at many conferences. She holds a Ph.D. from University Rennes1 and was a post-doc at the Mathematical Sciences Research Institute in Berkeley, California.

Author : Louis Antoine Victor De Cleene
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.64/5 ( download)

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Download or read book On Triangles Circumscribed about a Conic and Inscribed in a Cubic Curve written by Louis Antoine Victor De Cleene and published by . This book was released on 1927 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Henry Seely White
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.46/5 ( download)

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Download or read book Plane Cubics and Irrational Covariant Cubics written by Henry Seely White and published by . This book was released on 1900 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : J.W. Rutter
Publisher : CRC Press
ISBN 13 : 9781584881667
Total Pages : 384 pages
Book Rating : 4.66/5 ( download)

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Download or read book Geometry of Curves written by J.W. Rutter and published by CRC Press. This book was released on 2000-02-23 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in the study of geometry is currently enjoying a resurgence-understandably so, as the study of curves was once the playground of some very great mathematicians. However, many of the subject's more exciting aspects require a somewhat advanced mathematics background. For the "fun stuff" to be accessible, we need to offer students an introduction with modest prerequisites, one that stimulates their interest and focuses on problem solving. Integrating parametric, algebraic, and projective curves into a single text, Geometry of Curves offers students a unique approach that provides a mathematical structure for solving problems, not just a catalog of theorems. The author begins with the basics, then takes students on a fascinating journey from conics, higher algebraic and transcendental curves, through the properties of parametric curves, the classification of limaçons, envelopes, and finally to projective curves, their relationship to algebraic curves, and their application to asymptotes and boundedness. The uniqueness of this treatment lies in its integration of the different types of curves, its use of analytic methods, and its generous number of examples, exercises, and illustrations. The result is a practical text, almost entirely self-contained, that not only imparts a deeper understanding of the theory, but inspires a heightened appreciation of geometry and interest in more advanced studies.

Author : Keith Kendig
Publisher : American Mathematical Soc.
ISBN 13 : 1470456834
Total Pages : 403 pages
Book Rating : 4.32/5 ( download)

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Download or read book Conics written by Keith Kendig and published by American Mathematical Soc.. This book was released on 2020-07-29 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book engages the reader in a journey of discovery through a spirited discussion among three characters: philosopher, teacher, and student. Throughout the book, philosopher pursues his dream of a unified theory of conics, where exceptions are banished. With a helpful teacher and examplehungry student, the trio soon finds that conics reveal much of their beauty when viewed over the complex numbers. It is profusely illustrated with pictures, workedout examples, and a CD containing 36 applets. Conics is written in an easy, conversational style, and many historical tidbits and other points of interest are scattered throughout the text. Many students can selfstudy the book without outside help. This book is ideal for anyone having a little exposure to linear algebra and complex numbers.

Author : Charles Clayton Grove
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.79/5 ( download)

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Download or read book The Syzygetic Pencil of Cubics with a New Geometrical Development of Its Hesse Group, G216 written by Charles Clayton Grove and published by . This book was released on 1907 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Niccolo Guicciardini
Publisher : MIT Press
ISBN 13 : 0262291657
Total Pages : 449 pages
Book Rating : 4.51/5 ( download)

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Download or read book Isaac Newton on Mathematical Certainty and Method written by Niccolo Guicciardini and published by MIT Press. This book was released on 2011-08-19 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: An analysis of Newton's mathematical work, from early discoveries to mature reflections, and a discussion of Newton's views on the role and nature of mathematics. Historians of mathematics have devoted considerable attention to Isaac Newton's work on algebra, series, fluxions, quadratures, and geometry. In Isaac Newton on Mathematical Certainty and Method, Niccolò Guicciardini examines a critical aspect of Newton's work that has not been tightly connected to Newton's actual practice: his philosophy of mathematics. Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes's Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. Guicciardini shows how Newton carefully positioned himself against two giants in the “common” and “new” analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity's legitimate heir, thereby distancing himself from the moderns. Guicciardini reconstructs Newton's own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton's works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton's understanding of method and his mathematical work then reveal themselves through Guicciardini's careful analysis of selected examples. Isaac Newton on Mathematical Certainty and Method uncovers what mathematics was for Newton, and what being a mathematician meant to him.