Intermediate Geometry
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Introduction to Geometry
Author | : Richard Rusczyk |
Publisher | : Aops Incorporated |
Total Pages | : 557 |
Release | : 2007-07-01 |
Genre | : Juvenile Nonfiction |
ISBN | : 9781934124086 |
Elementary Geometry from an Advanced Standpoint
Author | : Edwin E. Moise |
Publisher | : Addison Wesley |
Total Pages | : 520 |
Release | : 1990 |
Genre | : Business & Economics |
ISBN | : |
Students can rely on Moise's clear and thorough presentation of basic geometry theorems. The author assumes that students have no previous knowledge of the subject and presents the basics of geometry from the ground up. This comprehensive approach gives instructors flexibility in teaching. For example, an advanced class may progress rapidly through Chapters 1-7 and devote most of its time to the material presented in Chapters 8, 10, 14, 19, and 20. Similarly, a less advanced class may go carefully through Chapters 1-7, and omit some of the more difficult chapters, such as 20 and 24.
Challenging Problems in Geometry
Author | : Alfred S. Posamentier |
Publisher | : Courier Corporation |
Total Pages | : 275 |
Release | : 2012-04-30 |
Genre | : Mathematics |
ISBN | : 0486134865 |
Collection of nearly 200 unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency and more. Arranged in order of difficulty. Detailed solutions.
Advanced Euclidean Geometry
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.
Euclidean Geometry in Mathematical Olympiads
Author | : Evan Chen |
Publisher | : American Mathematical Soc. |
Total Pages | : 311 |
Release | : 2021-08-23 |
Genre | : Education |
ISBN | : 1470466201 |
This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads or for teachers looking for a text for an honor class.
Higher Geometry
Author | : Frederick Shenstone Woods |
Publisher | : |
Total Pages | : 446 |
Release | : 1922 |
Genre | : Geometry, Analytic |
ISBN | : |
Open Middle Math
Author | : Robert Kaplinsky |
Publisher | : Taylor & Francis |
Total Pages | : 193 |
Release | : 2023-10-10 |
Genre | : Education |
ISBN | : 1003839886 |
This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking.
Methods of Geometry
Author | : James T. Smith |
Publisher | : John Wiley & Sons |
Total Pages | : 486 |
Release | : 2011-03-01 |
Genre | : Mathematics |
ISBN | : 1118031032 |
A practical, accessible introduction to advanced geometryExceptionally well-written and filled with historical andbibliographic notes, Methods of Geometry presents a practical andproof-oriented approach. The author develops a wide range ofsubject areas at an intermediate level and explains how theoriesthat underlie many fields of advanced mathematics ultimately leadto applications in science and engineering. Foundations, basicEuclidean geometry, and transformations are discussed in detail andapplied to study advanced plane geometry, polyhedra, isometries,similarities, and symmetry. An excellent introduction to advancedconcepts as well as a reference to techniques for use inindependent study and research, Methods of Geometry alsofeatures: Ample exercises designed to promote effective problem-solvingstrategies Insight into novel uses of Euclidean geometry More than 300 figures accompanying definitions and proofs A comprehensive and annotated bibliography Appendices reviewing vector and matrix algebra, least upperbound principle, and equivalence relations An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department.
Geometry Revisited
Author | : H. S. M. Coxeter |
Publisher | : American Mathematical Society |
Total Pages | : 193 |
Release | : 2021-12-30 |
Genre | : Mathematics |
ISBN | : 1470466414 |
Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.