Geometry in Action
Geometry in Action

Author: Clark Kimberling

Publisher: Springer Science & Business Media

Published: 2003

Total Pages: 212

ISBN-13: 9781931914024

DOWNLOAD EBOOK

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.

Modern Geometric Structures and Fields
Modern Geometric Structures and Fields

Author: Сергей Петрович Новиков

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 658

ISBN-13: 0821839292

DOWNLOAD EBOOK

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.

A Natural History of Shells
A Natural History of Shells

Author: Geerat J. Vermeij

Publisher: Princeton University Press

Published: 1995-04-23

Total Pages: 240

ISBN-13: 9780691001678

DOWNLOAD EBOOK

From “one of the master naturalists of our time” (American Scientist), a fascinating exploration of what seashells reveal about biology, evolution, and the history of life Geerat Vermeij wrote this “celebration of shells” to share his enthusiasm for these supremely elegant creations and what they can teach us about nature. Most popular books on shells emphasize the identification of species, but Vermeij uses shells as a way to explore major ideas in biology. How are shells built? How do they work? And how did they evolve? With lucidity and charm, the MacArthur-winning evolutionary biologist reveals how shells give us insights into the lives of animals today and in the distant geological past.

Variations on a Theme of Borel
Variations on a Theme of Borel

Author: Shmuel Weinberger

Publisher: Cambridge University Press

Published: 2022-12-08

Total Pages: 366

ISBN-13: 1108916848

DOWNLOAD EBOOK

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.

Geometric Puzzle Design
Geometric Puzzle Design

Author: Stewart Coffin

Publisher: CRC Press

Published: 2016-04-19

Total Pages: 222

ISBN-13: 1568814992

DOWNLOAD EBOOK

This book discusses how to design "good" geometric puzzles: two-dimensional dissection puzzles, polyhedral dissections, and burrs. It outlines major categories of geometric puzzles and provides examples, sometimes going into the history and philosophy of those examples. The author presents challenges and thoughtful questions, as well as practical d

A Natural History of Shells
A Natural History of Shells

Author: Geerat Vermeij

Publisher: Princeton University Press

Published: 2021-09-28

Total Pages: 236

ISBN-13: 0691229244

DOWNLOAD EBOOK

"With a new preface by the author"--Title page.

Introduction to Global Variational Geometry
Introduction to Global Variational Geometry

Author: Demeter Krupka

Publisher: Springer

Published: 2015-01-13

Total Pages: 366

ISBN-13: 9462390738

DOWNLOAD EBOOK

The book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. Emphasis is placed on the foundations of the theory of variational functionals on fibered manifolds - relevant geometric structures for variational principles in geometry, physical field theory and higher-order fibered mechanics. The book chapters include: - foundations of jet bundles and analysis of differential forms and vector fields on jet bundles, - the theory of higher-order integral variational functionals for sections of a fibred space, the (global) first variational formula in infinitesimal and integral forms- extremal conditions and the discussion of Noether symmetries and generalizations,- the inverse problems of the calculus of variations of Helmholtz type- variational sequence theory and its consequences for the global inverse problem (cohomology conditions)- examples of variational functionals of mathematical physics. Complete formulations and proofs of all basic assertions are given, based on theorems of global analysis explained in the Appendix.