Review: A New Conception of Geometry

A New Conception of Geometry by Prof Jingzhong Zhang
My rating: 3 of 5 stars

Here Professor Zhang shares a toolkit for solving geometry problems based on methods “used successfully by Chinese students training for the International Mathematical Olympiads.” Indeed, many examples and exercises draw on problems presented at Olympiads over the decades. These tools emerge in the proof-driven development of nine theorems with somewhat idiosyncratic names such as Co-Side Theorem, Co-Angle Converse Theorem, his often-applied Area Method, etc. Some more of the language with room for improvement in this translated work includes counterexamples being “thinking from the contrary” and line segments being “lines” while a line is an “extension line”...

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