by Robert Sharpley
Publisher: University of South Carolina 2008
Number of pages: 230
This course is a study of modern geometry as a logical system based upon postulates and undefined terms. Projective geometry, theorems of Desargues and Pappus, conics, transformation theory, affine geometry, Euclidean geometry, non-Euclidean geometries, and topology.
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by Wong Yan Loi - National University of Singapore
Contents: A Brief History of Greek Mathematics; Basic Results in Book I of the Elements; Triangles; Quadrilaterals; Concurrence; Collinearity; Circles; Using Coordinates; Inversive Geometry; Models and Basic Results of Hyperbolic Geometry.
by John O'Connor - University of St Andrews
Contents: Foundations; Linear groups; Isometries of Rn; Isometries of the line; Isometries of the plane; Isometries in 3 dimensions; Symmetry groups in the plane; Platonic solids; Finite symmetry groups of R3; Full finite symmetry groups in R3; etc.
by Robert J. Lang
Origami is the art of folding sheets of paper into interesting and beautiful shapes. In this text the author presents a variety of techniques for origami geometric constructions. The field has surprising connections to other branches of mathematics.
by Sigurdur Helgason - Birkhauser Boston
The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications.