Geometry

From the reviews of the second edition: "Devised primarily for future teachers of mathematics, but to be enjoyed by all lovers of geometry, including professional geometers, who will likely find something new in the historical part, this book renders an essential service to the mathematical community by presenting the story of geometry in two equal halves, the first half surveying its history up to Descartes and the second one presenting the version of geometry that emerged from the axiomatic revolution of the late 19th century, with an emphasis on algebraic geometry." (Victor V. Pambuccian, Zentralblatt MATH, Vol. 1202, 2011)

• Part I A Cultural Heritage: 1 Early Beginnings.- 2 The Great River Civilizations.- 3 Greek and Hellenic Geometry.- 4 Geometry in the Hellenistic Era.- 5 Arabic Mathematics and Geometry.- 6 The Geometry of Yesterday and Today.- 7 Geometry and the Real World.- Part II Introduction to Geometry: 8 Axiomatic Geometry.- 9 Axiomatic Projective Geometry.- 10 Models for Non-Euclidean Geometry.- 11 Making Things Precise.- 12 Projective Space.- 13 Geometry in the Affine and the Projective Plane.- 14 Algebraic Curves of Higher Degrees in the Affine Plane R2.- 15 Higher Geometry in the Projective Plane.- 16 Sharpening the Sword of Algebra.- 17 Constructions with Straightedge and Compass.- 18 Fractal Geometry.- 19 Catastrophe Theory.- 20 General Polyhedra and Tesselations, and their Groups of Symmetry.- 21 Hints and Solutions to some of the Excercises.- References.- Index