Exercises On Euclid And In Modern Geometry
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Author | : M. N. Aref |
Publisher | : Courier Corporation |
Total Pages | : 274 |
Release | : 2010-01-01 |
Genre | : Mathematics |
ISBN | : 0486477207 |
Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. Each chapter covers a different aspect of Euclidean geometry, lists relevant theorems and corollaries, and states and proves many propositions. Includes more than 200 problems, hints, and solutions. 1968 edition.
Author | : Roger A. Johnson |
Publisher | : Courier Corporation |
Total Pages | : 338 |
Release | : 2013-01-08 |
Genre | : Mathematics |
ISBN | : 048615498X |
This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.
Author | : John M. Lee |
Publisher | : American Mathematical Soc. |
Total Pages | : 490 |
Release | : 2013-04-10 |
Genre | : Mathematics |
ISBN | : 0821884786 |
The story of geometry is the story of mathematics itself: Euclidean geometry was the first branch of mathematics to be systematically studied and placed on a firm logical foundation, and it is the prototype for the axiomatic method that lies at the foundation of modern mathematics. It has been taught to students for more than two millennia as a mode of logical thought. This book tells the story of how the axiomatic method has progressed from Euclid's time to ours, as a way of understanding what mathematics is, how we read and evaluate mathematical arguments, and why mathematics has achieved the level of certainty it has. It is designed primarily for advanced undergraduates who plan to teach secondary school geometry, but it should also provide something of interest to anyone who wishes to understand geometry and the axiomatic method better. It introduces a modern, rigorous, axiomatic treatment of Euclidean and (to a lesser extent) non-Euclidean geometries, offering students ample opportunities to practice reading and writing proofs while at the same time developing most of the concrete geometric relationships that secondary teachers will need to know in the classroom. -- P. [4] of cover.
Author | : George A. Jennings |
Publisher | : Springer Science & Business Media |
Total Pages | : 193 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461208556 |
This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry. Additionally, it covers the two important areas of non-Euclidean geometry, spherical geometry and projective geometry, as well as emphasising transformations, and conics and planetary orbits. Much emphasis is placed on applications throughout the book, which motivate the topics, and many additional applications are given in the exercises. It makes an excellent introduction for those who need to know how geometry is used in addition to its formal theory.
Author | : Robert Kaplan |
Publisher | : Bloomsbury Publishing USA |
Total Pages | : 417 |
Release | : 2014-02-04 |
Genre | : Mathematics |
ISBN | : 1608198693 |
Traces the development of mathematical thinking and describes the characteristics of the "republic of numbers" in terms of humankind's fascination with, and growing knowledge of, infinity.
Author | : Clayton W. Dodge |
Publisher | : Courier Corporation |
Total Pages | : 306 |
Release | : 2012-04-26 |
Genre | : Mathematics |
ISBN | : 0486138429 |
This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
Author | : Robin Hartshorne |
Publisher | : Springer Science & Business Media |
Total Pages | : 535 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 0387226761 |
This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.
Author | : Edward John Specht |
Publisher | : Birkhäuser |
Total Pages | : 537 |
Release | : 2015-12-31 |
Genre | : Mathematics |
ISBN | : 3319237756 |
In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of these, including all that are needed for this development, are available online at the homepage for the book at www.springer.com. Supplementary material is available online covering construction of complex numbers, arc length, the circular functions, angle measure, and the polygonal form of the Jordan Curve theorem. Euclidean Geometry and Its Subgeometries is intended for advanced students and mature mathematicians, but the proofs are thoroughly worked out to make it accessible to undergraduate students as well. It can be regarded as a completion, updating, and expansion of Hilbert's work, filling a gap in the existing literature.
Author | : Kathryn Goulding |
Publisher | : |
Total Pages | : |
Release | : 2017-09-15 |
Genre | : |
ISBN | : 9780692925959 |
The instructor's edition of Euclid's Elements With Exercises is intended as a guide for anyone teaching Euclid for the first time. Although it could be used by anyone, it was assembled and written with small schools or homeschooling groups in mind. In addition to containing the first six books in exactly the format of the student edition (also available on Amazon), the instructor's edition provides a concise overview of the course, including suggestions for conducting the class, a discussion of the organization of the material, brief comments on supplemental and memory work, and other details about which a new instructor might have questions. It also has notes for the teacher on each of the six books of the Elements, notes on selected exercises, and an appendix explaining the basics of formal reasoning, including an explanation of the converse and contrapositive of a statement and the concept of an indirect proof, which occurs early in Book I. The primary difference between this work and Euclid's Elements as it is usually presented (aside from the fact that there are some exercises), is that, while all of Books I - VI are included in the book, some propositions are omitted in the main body of the text (all omitted propositions are in Appendix A). This was done in order to be able to finish in two semesters all the plane geometry that would normally be covered in a modern geometry class. It should be noted, of course, that the flow of logic of the propositions is never interrupted. This book was not designed for the purist. Although it is pure Euclid and contains all of the first six books, it may offend the sensibilities of some who love Euclid (as the assembler/author does) to fail to place Book II in the expected flow of the main body of the text. For anyone not under a time constraint, or anyone moving quickly through the text, the author strongly recommends the inclusion of Book II in the course flow.
Author | : J. MacDowell |
Publisher | : |
Total Pages | : |
Release | : 1881 |
Genre | : |
ISBN | : |