Geometric inequalities /
Leng, Gangsong,
Geometric inequalities / Gangsong Leng, Shanghai University, China ; translated by Yongming Liu, East China Normal University, China. - Singapore : East China National University Press : World Scientific Publishing Co., Shanghai, China, Hackensack, NJ, 2016. - viii, 136 pages : illustrations ; 24 cm. - Mathematical Olympiad series ; vol. 12 . - Mathematical Olympiad series ; v. 12. .
Cover
Halftitle
Title Page
Copyright
Contents
Preface
Chapter 1 The method of segment replacement for distance inequalities
Chapter 2 Ptolemy’s inequality and its application
Chapter 3 Inequality for the inscribed quadrilateral
Chapter 4 The area inequality for special polygons
Chapter 5 Linear geometric inequalities
Chapter 6 Algebraic methods
Chapter 7 Isoperimetric and extremal value problem
Chapter 8 Embed inequality and inequality for moment of inertia
Chapter 9 Locus problem of Tsintsifas’s inequality
Chapter 10 Shum’s minimal circle problem
Chapter 11 Inequalities for tetrahedron
Answers and hints to selected exercises
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.
9789814704137 981470413X 9789814696487 (pbk.) 981469648X (pbk.)
Geometry, Algebraic
Geometry, Plane
Inequalities (Mathematics)
Geometry, Plane.
Inequalities (Mathematics)--Problems, exercises, etc.--Problems, exercises, etc.--Problems, exercises, etc.
516.4 / LEN
Geometric inequalities / Gangsong Leng, Shanghai University, China ; translated by Yongming Liu, East China Normal University, China. - Singapore : East China National University Press : World Scientific Publishing Co., Shanghai, China, Hackensack, NJ, 2016. - viii, 136 pages : illustrations ; 24 cm. - Mathematical Olympiad series ; vol. 12 . - Mathematical Olympiad series ; v. 12. .
Cover
Halftitle
Title Page
Copyright
Contents
Preface
Chapter 1 The method of segment replacement for distance inequalities
Chapter 2 Ptolemy’s inequality and its application
Chapter 3 Inequality for the inscribed quadrilateral
Chapter 4 The area inequality for special polygons
Chapter 5 Linear geometric inequalities
Chapter 6 Algebraic methods
Chapter 7 Isoperimetric and extremal value problem
Chapter 8 Embed inequality and inequality for moment of inertia
Chapter 9 Locus problem of Tsintsifas’s inequality
Chapter 10 Shum’s minimal circle problem
Chapter 11 Inequalities for tetrahedron
Answers and hints to selected exercises
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.
9789814704137 981470413X 9789814696487 (pbk.) 981469648X (pbk.)
Geometry, Algebraic
Geometry, Plane
Inequalities (Mathematics)
Geometry, Plane.
Inequalities (Mathematics)--Problems, exercises, etc.--Problems, exercises, etc.--Problems, exercises, etc.
516.4 / LEN