Hungarian Problem Book III
György Hajós, G. Neukomm, Andy Liu, János Surányi
Cambridge University Press, 9 d’ag. 2001 - 142 pàgines
This book contains the problems and solutions of a famous Hungarian mathematics competition for high school students, from 1929 to 1943. The competition is the oldest in the world, and started in 1894. Two earlier volumes in this series contain the papers up to 1928, and further volumes are planned. The current edition adds a lot of background material which is helpful for solving the problems therein and beyond. Multiple solutions to each problem are exhibited, often with discussions of necessary background material or further remarks. This feature will increase the appeal of the book to experienced mathematicians as well as the beginners for whom it is primarily intended.
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1-filler AA Theorem ABC and DEF acute triangle altitude arithmetic mean binary relation called center of symmetry centroid circumcenter circumcircle circumradius Combinatorics common divisor competition complex number cos2 DEF are congruent denote diameter distance divides divisible edges elements Equality holds equidistant equilateral triangle Exterior Angle filler follows geometry George Berzsenyi graph greatest common divisor Hence triangles highest power Hungarian Problem Book induction hypothesis intersect lattice points Mathematical Induction maximum Mean Inequality median of triangle midpoint of BC minimum multiple orthocenter pairs parallelogram Pascal's Formula perimeter permutation pigeons plane point inside polygon positive integers Proof Prove radical axis radius Rearrangement Inequality rectangles respectively result SAS Postulate Second Solution semicircle shown in Figure side lengths Similarly Suppose symmetric relation tangent triangle ABC Triangle Inequality Value Principle vector vertex vertices Well-Ordering Principle ZABC ZACB ZAOB ZBCA