Book review: Exploring Classical Greek Construction Problems with Interactive Geometry Software
This is a review of Exploring Classical Greek Construction Problems with Interactive Geometry Software by Meskens and Tytgat (2017).
As the name implies, the book is devoted to an analysis of classical Greek construction problems. In particular the core of the book contains three chapters. Chapter 4 considers The Delian Problem, also known as duplicating the cube; Chapter 5 considers Trisecting an angle and Chapter 6 Squaring the circle. To set the scene Chapter 2 gives a Genesis of Geometry, including a discussion of mechanical construction aids. This leads to a more formal discussion in Chapter 3 of constructions with compass and straightedge. The last two chapters round off the story by discussing constructible numbers and the regular polygons. Despite the title, the book actually contains a broad range of core ideas from the heart of mathematics. For example, Chapter 6 has an interesting discussion of infinitesimal arguments, related to the calculation of area. There is also some...
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