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264304399
Volume 4: Geometry (Rigorous Elementary Mathematics, Second Edition)
Item #:
264304399
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Volume 4: Geometry builds the subject from the ground up using a computational approach to elevate your understanding of geometry.
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- Geometry is one of the four pillars of mathematical contests and olympiads. Volume 4: Geometry, Second Edition builds the subject from the ground up. It takes a computational approach to the subject, by utilizing trigonometry, complex numbers, and vectors. There are initial chapters on lines, angles, and congruence and similarity transformations. There is a chapter on circles, which includes proofs of the inscribed angle theorem and power of a point theorem using complex numbers. A special chapter delves into cevians and triangle centres. Geometric objects, such as triangles, convex and concave polygons, and polyhedra are studied and classified. The final chapter includes a detailed study of conic sections via bivariate quadratics, including a complete proof of the classification of directrix-eccentricity-focal parameter triples for ellipses, parabolas, and hyperbolas. The three recurring themes are: writing the same object in multiple ways, breaking up equality using antisymmetry, and using equivalence relations. There are dozens of substantive problems included for the reader’s practice, with complete solutions provided. This second edition includes additional theorems and problems, refreshed diagrams, and corrections. It is suggested that the book be read by students and teachers who have prior experience with mathematical proofs and problem-solving.
| Publisher | Existsforall Academy Inc. |
| Publication date | June 8, 2026 |
| Language | English |
| Print length | 207 pages |
| ISBN-10 | 1067814213 |
| ISBN-13 | 978-1067814212 |
| Item Weight | 1.4 pounds (640 grams) |
| Dimensions | 8.27 x 0.47 x 11.69 inches (21 x 1.2 x 29.7 cm) |
| Book 4 of 5 | Rigorous Elementary Mathematics, Second Edition |
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Volume 4: Geometry (Rigorous Elementary Mathematics, Second Edition)
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Features & Benefits
- Comprehensive guide to geometry, ideal for contests and olympiads.
- Utilizes trigonometry, complex numbers, and vectors for a deep understanding.
- Includes detailed chapters on lines, angles, circles, and triangle centres.
- Features geometric objects classification: triangles, polygons, polyhedra.
- Final chapter focuses on conic sections with proofs and classifications.
- Dozens of practice problems with complete solutions are included.
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