Geometric Inequalities In Mathematical Olympiad And Competitions
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| Author | : Radmila Bulajich Manfrino |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 214 |
| Release | : 2010-01-01 |
| Genre | : Mathematics |
| ISBN | : 303460050X |
This book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad. The book has been organized in four chapters which have each of them a different character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. However, where it is possible to provide a geometric interpretation, we include it as we go along. We emphasize the importance of some of these inequalities, such as the inequality between the arithmetic mean and the geometric mean, the Cauchy-Schwarz inequality, the rearrangementinequality, the Jensen inequality, the Muirhead theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad problems. We also emphasize how the substitution strategy is used to deduce several inequalities.
| Author | : Hayk Sedrakyan |
| Publisher | : Springer |
| Total Pages | : 454 |
| Release | : 2017-05-27 |
| Genre | : Mathematics |
| ISBN | : 3319550802 |
This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities.
| Author | : Gangsong Leng |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 145 |
| Release | : 2015-10-21 |
| Genre | : Mathematics |
| ISBN | : 9814696501 |
In China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they won the first place almost every year.The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO.This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on Geometric Inequality problems such as inequality for the inscribed quadrilateral, the area inequality for special polygons, linear geometric inequalities, etc.
| Author | : Zdravko Cvetkovski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 439 |
| Release | : 2012-01-06 |
| Genre | : Mathematics |
| ISBN | : 3642237924 |
This work is about inequalities which play an important role in mathematical Olympiads. It contains 175 solved problems in the form of exercises and, in addition, 310 solved problems. The book also covers the theoretical background of the most important theorems and techniques required for solving inequalities. It is written for all middle and high-school students, as well as for graduate and undergraduate students. School teachers and trainers for mathematical competitions will also gain benefit from this book.
| 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.
| Author | : Alijadallah Belabess |
| Publisher | : |
| Total Pages | : 242 |
| Release | : 2019-03-14 |
| Genre | : Mathematics |
| ISBN | : 9781794193925 |
This book contains a unique collection of new inequalities that were specifically imagined by the author to challenge the boundaries of curiosity and imagination. The inequalities are extremely beautiful and sharp, and the book covers various topics from 3 and 4 variables inequalities, symmetric and non-symmetric inequalities to geometric inequalities. Many of the exercises are presented with detailed solutions covering a variety of must-know old and new techniques in tackling Olympiad problems. The book contains also a variety of unsolved exercises which were left to the reader as additional challenges. Most importantly, the book deals with the daunting topic of asymmetric inequalities where most classical approaches fail. The book has been organised in five chapters. In the first one, we presented a collection of classical algebraic and geometric inequalities such as Cauchy-Schwarz, Cheybeshev's, Newton's, Bernoulli's, Euler's, Walker's inequalities among others. These are the classical inequalities that any student should master if he is aiming for a medal at Mathematical Olympiad competitions. The second and third chapters deal respectively with 3 and 4 variables inequalities covering both symmetric and asymmetric inequalities. The fourth chapter is about Geometric inequalities involving triangle sides, medians, altitudes, internal bisectors, areas, perimeters, orthic triangles, angles, circumradius, inradius...The last chapter contains detailed solutions to the proposed problems with more than one solution for some of the inequalities.
| Author | : Adrian Andreescu |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2017 |
| Genre | : |
| ISBN | : 9780979926983 |
For the curious reader looking to sharpen their arsenal of mathematical strategies on the Olympiad level, 113 Geometric Inequalities from the AwesomeMath Summer Program is a valuable addition. This problem-solving methodology prompts key ideas in other domains such as calculus or complex numbers as the solutions are usually nonstandard in a geometric sense. Nevertheless, trying your hand at these types of inequalities consolidates your mathematical reasoning while exposing you to a broad range of problems, all teeming with insightful inequality-type solutions.
| Author | : Alexander Sarana |
| Publisher | : Courier Dover Publications |
| Total Pages | : 430 |
| Release | : 2020-08-12 |
| Genre | : Mathematics |
| ISBN | : 0486842533 |
This original work discusses mathematical methods needed by undergraduates in the United States and Canada preparing for competitions at the level of the International Mathematical Olympiad (IMO) and the Putnam Competition. The six-part treatment covers counting methods, number theory, inequalities and the theory of equations, metrical geometry, analysis, and number representations and logic. Includes problems with solutions plus 1,000 problems for students to finish themselves.
| Author | : Hai Chau Le |
| Publisher | : World Scientific |
| Total Pages | : 331 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 9814289590 |
Vietnam has actively organized the National Competition in Mathematics and since 1962, the Vietnamese Mathematical Olympiad (VMO). On the global stage, Vietnam has also competed in the International Mathematical Olympiad (IMO) since 1974 and constantly emerged as one of the top ten. To inspire and further challenge readers, we have gathered in this book selected problems of the VMO from 1962 to 2008. A number of Selection Test problems are also included to aid in the formation and training of a national team for IMO. The book is highly useful for high school students and teachers, coaches and instructors preparing for mathematical olympiads, as well as non-experts simply interested in having the edge over their opponents in mathematical competitions.
| Author | : B.J. Venkatachala |
| Publisher | : Springer |
| Total Pages | : 527 |
| Release | : 2018-05-09 |
| Genre | : Mathematics |
| ISBN | : 9811087326 |
This book discusses about the basic topics on inequalities and their applications. These include the arithmetic mean–geometric mean inequality, Cauchy–Schwarz inequality, Chebyshev inequality, rearrangement inequality, convex and concave functions and Muirhead's theorem. The book contains over 400 problems with their solutions. A chapter on geometric inequalities is a special feature of this book. Most of these problems are from International Mathematical Olympiads and from many national mathematical Olympiads. The book is intended to help students who are preparing for various mathematical competitions. It is also a good source book for graduate students who are consolidating their knowledge of inequalities and their applications.
