In this amazing cache of designs, arresting displays of geometrics explode into thousands of fascinating variations. Each of forty-one original black-and-white motifs is spun into three pages of adaptations, offering strikingly different variations on the original theme. More than 4,300 images build upon basic geometric shapes, transforming circles, squares, rectangles, and triangles into intricate patterns that form kaleidoscopic designs, optical illusions, and hypnotic abstracts. A versatile resource for graphics, art, and craft projects, this collection offers not only a wealth of images for immediate practical use but also an excellent reference for design inspiration.

The calculus of variations is a beautiful subject with a rich history and with origins in the minimization problems of calculus. Although it is now at the core of many modern mathematical fields, it does not have a well-defined place in most undergraduate mathematics curricula. This volume should nevertheless give the undergraduate reader a sense of its great character and importance. Interesting functionals, such as area or energy, often give rise to problems whose most natural solution occurs by differentiating a one-parameter family of variations of some function. The critical points of the functional are related to the solutions of the associated Euler-Lagrange equation. These differential equations are at the heart of the calculus of variations and its applications to wave mechanics, minimal surfaces, soap bubbles, and modeling traffic flow. All are readily accessible to advanced undergraduates. This book is derived from a workshop sponsored by Rice University. It is suitable for advanced undergraduates, graduate students and research mathematicians interested in the calculus of variations and its applications to other subjects.

Geometry in Action uses Sketchpad? to awaken student creativity through discovery-based learning. It supplements any college geometry course in which The Geometer's Sketchpad is used. All students must have access to The Geometer's Sketchpad.Each book is packaged with a CD-ROM for students that illustrates what is meant by geometry in action. Students explore 27 sketches prepared by the author to demonstrate Sketchpad's capabilities by dragging points to see shifts in graphs, by animating tesselations to create new patterns, and much, much more! Also included on this CD is the Poincare Disk, a Sketchpad file used to dig deeper into non-Euclidean geometry with The Geometer's Sketchpad.

Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.

Geometric constructions have been a popular part of mathematics throughout history. The first chapter here is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never learned. The second chapter formalises Plato's game, and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, a compass, toothpicks, a ruler and dividers, a marked rule, or a tomahawk, ending in a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics, teaching a little geometry and a little algebra along the way. This is as much an algebra book as it is a geometry book, yet since all the algebra and geometry needed is developed within the text, very little mathematical background is required. This text has been class tested for several semesters with a master's level class for secondary teachers.

In the middle of the last century, after hearing a talk of Mostow on one of his rigidity theorems, Borel conjectured in a letter to Serre a purely topological version of rigidity for aspherical manifolds (i.e. manifolds with contractible universal covers). The Borel conjecture is now one of the central problems of topology with many implications for manifolds that need not be aspherical. Since then, the theory of rigidity has vastly expanded in both precision and scope. This book rethinks the implications of accepting his heuristic as a source of ideas. Doing so leads to many variants of the original conjecture - some true, some false, and some that remain conjectural. The author explores this collection of ideas, following them where they lead whether into rigidity theory in its differential geometric and representation theoretic forms, or geometric group theory, metric geometry, global analysis, algebraic geometry, K-theory, or controlled topology.