Gao, X.-S., Wang, D., Qiu, Z., Yang, H.: Equation Solving and Mechanical Proving: Problem Solving with MMP. Springer, New York, Berlin, Heidelberg (2000) World Scientific, Singapore (1994)Ĭox, D., Little, J., O’shea, D.: Ideal, Varieties, and Algorithms, 3rd edn. Academic Press, San Diego (1989)Ĭhou, S.-C., Gao, X.-S., Zhang, J.-Z.: Machine Proofs in Geometry: Automated Production of Readable Proofs for Geometry Theorems. (eds.) Resolution of equations in algebraic structures, pp. Reidel Publishing Company, Dordrecht (1988)Ĭhou, S.-C., Schelter, W.F., Yang, J.-G.: Characteristic sets and Gröbner bases in geometry theorem proving. Reidel (1985)Ĭhou, S.-C.: Mechanical Geometry Theorem Proving. In: Recent Trends in Multidimensional Systems Theory. This book is especially suitable for students preparing for national or international mathematical olympiads, or for teachers looking for a text for an honors class.Buchberger, B.: Gröbner bases: an algorithmic method in polynomial ideal theory.
The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions.
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 emphasis of this book is placed squarely on the problems. The exposition is friendly and relaxed, and accompanied by over 248 beautifully drawn figures. 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. 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. 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. Topics covered include cyclic quadrilaterals, power of a point, homothety, and triangle centers. This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage.
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