Exploring classical Greek construction problems with interactive geometry software / Ad Meskens, Paul Tytgat.

Preface; Some preliminary remarks; Contents; List of Figures[1]; 1 Introduction; 1.1 Introduction; 1.2 Interactive Geometry Software (IGS); 1.3 Polar coordinates; 2 The Genesis of Geometry; 2.1 Greeks and their Geometry; 2.2 Examples from Plato's hierarchy; 2.3 Adrian van Roomen and Apollonius' Problem; 2.4 Mechanical construction aids; 2.5 Neusis; 3 Compass and straightedge constructions; 3.1 Euclid's Elements; 3.2 Compass and straightedge constructions; 3.3 François Viète and Apollonius' Problem; 4 The Delian Problem; 4.1 Delos and its altar; 4.2 Wine gauging

4.3 Doubling the cube with a neusis5 Trisecting an angle; 5.1 Nicomedes' conchoid; 5.2 Archimedes; 5.3 The first Archimedean trisection; 5.4 The Archimedean spiral; 5.5 The Flemish Jesuits; 5.6 Hippias of Elis and the quadratrix; 6 Squaring the circle; 6.1 Archimedes' spiral revisited; 6.2 Dinostratus' quadratrix; 6.3 Hippocrates' lunes; 6.4 Franco of Liège, the demise of mathematics; 6.5 Nicolas of Cusa; 6.6 Archimedes' approximation; 6.7 Adriaan van Roomen and Ludolff van Ceulen; 6.8 Kepler's use of infinitesimal methods; 6.9 Gregory of St Vincent; 7 Constructible numbers

7.1 Constructing numbers7.2 The theory of equations; 7.3 Squarable lunes; 7.4 Squaring the circle is different …; 8 The Cinderella of regular polygons; 8.1 The inconstructibility of the heptagon; 8.2 The relation with the trisection; 8.3 A neusis for the heptagon; Servicepart; Solutions; References; Index