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Books > Science & Mathematics > Mathematics > Geometry > General
Origami, the art of paper folding, has a rich mathematical theory.
Early investigations go back to at least the 1930s, but the
twenty-first century has seen a remarkable blossoming of the
mathematics of folding. Besides its use in describing origami and
designing new models, it is also finding real-world applications
from building nano-scale robots to deploying large solar arrays in
space. Written by a world expert on the subject, Origametry is the
first complete reference on the mathematics of origami. It brings
together historical results, modern developments, and future
directions into a cohesive whole. Over 180 figures illustrate the
constructions described while numerous 'diversions' provide
jumping-off points for readers to deepen their understanding. This
book is an essential reference for researchers of origami
mathematics and its applications in physics, engineering, and
design. Educators, students, and enthusiasts will also find much to
enjoy in this fascinating account of the mathematics of folding.
Beyond Einstein: Perspectives on Geometry, Gravitation, and
Cosmology explores the rich interplay between mathematical and
physical ideas by studying the interactions of major actors and the
roles of important research communities over the course of the last
century.
Extrinsic geometric flows are characterized by a submanifold
evolving in an ambient space with velocity determined by its
extrinsic curvature. The goal of this book is to give an extensive
introduction to a few of the most prominent extrinsic flows,
namely, the curve shortening flow, the mean curvature flow, the
Gauss curvature flow, the inverse-mean curvature flow, and fully
nonlinear flows of mean curvature and inverse-mean curvature type.
The authors highlight techniques and behaviors that frequently
arise in the study of these (and other) flows. To illustrate the
broad applicability of the techniques developed, they also consider
general classes of fully nonlinear curvature flows. The book is
written at the level of a graduate student who has had a basic
course in differential geometry and has some familiarity with
partial differential equations. It is intended also to be useful as
a reference for specialists. In general, the authors provide
detailed proofs, although for some more specialized results they
may only present the main ideas; in such cases, they provide
references for complete proofs. A brief survey of additional
topics, with extensive references, can be found in the notes and
commentary at the end of each chapter.
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