Tilings and Patterns
by E O Harriss
Publisher: Mathematicians.org.uk 2008
Number of pages: 43
Contents: Background Material (Euclidean Space, Delone Sets, Z-modules and lattices); Tilings of the plane (Periodic, Aperiodic, Penrose Tilings, Substitution Rules and Tiling, Matching Rules); Symbolic and Geometric tilings of the line (Combinatorics of Words, Letter substitution rules, Canonical Projection Tilings and Sturmian Sequences).
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by Derrick Norman Lehmer - Project Gutenberg
The book gives, in a simple way, the essentials of synthetic projective geometry. Enough examples have been provided to give the student a clear grasp of the theory. The student should have a thorough grounding in ordinary elementary geometry.
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 John C. Polking - Rice University
We are interested here in the geometry of an ordinary sphere. In plane geometry we study points, lines, triangles, polygons, etc. On the sphere there are no straight lines. Therefore it is natural to use great circles as replacements for lines.
by Maximilian Kreuzer - Technische Universitat Wien
From the table of contents: Topology (Homotopy, Manifolds, Surfaces, Homology, Intersection numbers and the mapping class group); Differentiable manifolds; Riemannian geometry; Vector bundles; Lie algebras and representations; Complex manifolds.