Mathematical Olympiad TreasuresMathematical Olympiad Treasures aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts in undergraduate mathematics. The book contains a stimulating collection of problems in the subjects of algebra, geometry, trigonometry, number theory and combinatorics. While it may be considered a sequel to "Mathematical Olympiad Challenges," the focus is on engaging a wider audience to apply techniques and strategies to real-world problems. Throughout the book students are encouraged to express their ideas, conjectures, and conclusions in writing. The goal is to help readers develop a host of new mathematical tools that will be useful beyond the classroom and in a number of disciplines. |
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3abc acquainted an+1 angle bisectors arithmetic sequence arithmetical progression boys Cauchy–Schwarz inequality circumcenter circumcircle collinear columns common difference contradiction convex quadrilateral cyclic quadrilateral deduce defined Denote diagonal digits distinct divisible divisors entries equiangular polygon equilateral triangle equivalent exists Find the locus function f geometrical sequence girls Hall’s condition hence induction inscribed circle integer and let interior least lemma Let ABCD Let x1 locus of points midpoint obtain odd integers orthocenters parallel parallelogram permutation point of intersection positive integer positive numbers positive real numbers prime number proof Prove the inequality rational number rearrangements inequality roots rows and different segment side BC side lengths Solution Consider solution in integers Solution Let Solution Observe Solution Suppose Solve the equation Springer Science+Business Media square Taking the conjugate theorem triangle ABC vertices yields