Euclidean Geometry in Mathematical Olympiads

Euclidean Geometry in Mathematical Olympiads

PDF Euclidean Geometry in Mathematical Olympiads Download

  • Author: Evan Chen
  • Publisher: American Mathematical Soc.
  • ISBN: 1470466201
  • Category : Education
  • Languages : en
  • Pages : 311

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.


Euclidean Geometry in Mathematical Olympiads

Euclidean Geometry in Mathematical Olympiads

PDF Euclidean Geometry in Mathematical Olympiads Download

  • Author: Evan Chen
  • Publisher: The Mathematical Association of America
  • ISBN: 0883858398
  • Category : Mathematics
  • Languages : en
  • Pages : 329

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 as 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.


Euclidean Geometry in Mathematical Olympiads

Euclidean Geometry in Mathematical Olympiads

PDF Euclidean Geometry in Mathematical Olympiads Download

  • Author: Evan Chen (Mathematician)
  • Publisher:
  • ISBN: 9781614444114
  • Category : Geometry
  • Languages : en
  • Pages : 311


Problem-Solving and Selected Topics in Euclidean Geometry

Problem-Solving and Selected Topics in Euclidean Geometry

PDF Problem-Solving and Selected Topics in Euclidean Geometry Download

  • Author: Sotirios E. Louridas
  • Publisher: Springer Science & Business Media
  • ISBN: 1461472733
  • Category : Mathematics
  • Languages : en
  • Pages : 238

"Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry. Before the complete solution of every problem, a key idea is presented so that the reader will be able to provide the solution. Applications of the basic geometrical methods which include analysis, synthesis, construction and proof are given. Selected problems which have been given in mathematical olympiads or proposed in short lists in IMO's are discussed. In addition, a number of problems proposed by leading mathematicians in the subject are included here. The book also contains new problems with their solutions. The scope of the publication of the present book is to teach mathematical thinking through Geometry and to provide inspiration for both students and teachers to formulate "positive" conjectures and provide solutions.


Problems and Solutions in Euclidean Geometry

Problems and Solutions in Euclidean Geometry

PDF Problems and Solutions in Euclidean Geometry Download

  • Author: M. N. Aref
  • Publisher: Courier Corporation
  • ISBN: 0486477207
  • Category : Mathematics
  • Languages : en
  • Pages : 274

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.


Challenges in Geometry

Challenges in Geometry

PDF Challenges in Geometry Download

  • Author: Christopher J. Bradley
  • Publisher: OUP Oxford
  • ISBN: 0191524263
  • Category : Mathematics
  • Languages : en
  • Pages : 218

The International Mathematical Olympiad (IMO) is the World Championship Mathematics Competition for High School students and is held annually in a different country. More than eighty countries are involved. Containing numerous exercises, illustrations, hints and solutions, presented in a lucid and thought-provoking style, this text provides a wide range of skills required in competitions such as the Mathematical Olympiad. More than fifty problems in Euclidean geometry involving integers and rational numbers are presented. Early chapters cover elementary problems while later sections break new ground in certain areas and are a greater challenge for the more adventurous reader. The text is ideal for Mathematical Olympiad training and also serves as a supplementary text for students in pure mathematics, particularly number theory and geometry. Dr. Christopher Bradley was formerly a Fellow and Tutor in Mathematics at Jesus College, Oxford, Deputy Leader of the British Mathematical Olympiad Team and for several years Secretary of the British Mathematical Olympiad Committee.


Geometry Revisited

Geometry Revisited

PDF Geometry Revisited Download

  • Author: H. S. M. Coxeter
  • Publisher: American Mathematical Society
  • ISBN: 1470466414
  • Category : Mathematics
  • Languages : en
  • Pages : 193

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.


Plane Euclidean Geometry

Plane Euclidean Geometry

PDF Plane Euclidean Geometry Download

  • Author: Anthony Gardiner
  • Publisher: Anchor Books
  • ISBN: 9781906001186
  • Category : Euclid's Elements
  • Languages : en
  • Pages : 213


Problems of Number Theory in Mathematical Competitions

Problems of Number Theory in Mathematical Competitions

PDF Problems of Number Theory in Mathematical Competitions Download

  • Author: Hong-Bing Yu
  • Publisher: World Scientific
  • ISBN: 9814271144
  • Category : Mathematics
  • Languages : en
  • Pages : 115

Number theory is an important research field of mathematics. In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. They are flexible and diverse. In this book, the author introduces some basic concepts and methods in elementary number theory via problems in mathematical competitions. Readers are encouraged to try to solve the problems by themselves before they read the given solutions of examples. Only in this way can they truly appreciate the tricks of problem-solving.


Geometry in figures

Geometry in figures

PDF Geometry in figures Download

  • Author: Arseny V. Akopyan
  • Publisher: Createspace Independent Publishing Platform
  • ISBN: 9781548710781
  • Category : Geometry
  • Languages : en
  • Pages : 0

This book is a collection of theorems and problems in classical Euclidean geometry formulated in figures. It is intended for advanced high school and undergraduate students, teachers and all who like classical geometry. This is second, extended edition.