By Ulf Leonhardt
Appropriate for complicated undergraduate and graduate scholars of engineering, physics, and arithmetic and clinical researchers of every kind, this is often the 1st authoritative textual content on invisibility and the technology in the back of it. It introduces the mathematical foundations of differential geometry and demonstrates sensible purposes from basic relativity to electric and optical engineering. greater than a hundred full-color illustrations, plus workouts with suggestions.
desk of Contents
2. Fermat's precept
three. Differential Geometry
four. Maxwell's Equations
five. Geometries and Media
By Herbert Busemann
Starting with a short evaluation of notations and terminology, the textual content proceeds to convex curves, the theorems of Meusnier and Euler, extrinsic Gauss curvature, and the impact of the curvature at the neighborhood form of a floor. A bankruptcy at the Brunn-Minkowski concept and its functions is via examinations of intrinsic metrics, the metrics of convex hypersurfaces, geodesics, angles, triangulations, and the Gauss-Bonnet theorem. the ultimate bankruptcy explores the stress of convex polyhedra, the conclusion of polyhedral metrics, Weyl's challenge, neighborhood attention of metrics with non-negative curvature, open and closed surfaces, and smoothness of realizations.
By Chris McMullen
This colourful, visible creation to the fourth measurement offers a transparent clarification of the thoughts and various illustrations. it really is written with a slightly of character that makes this an enticing learn rather than a dry math textual content. The content material is particularly available, but even as exact adequate to fulfill the pursuits of complex readers. This booklet is dedicated to geometry; there are not any non secular or spiritual parts to this publication. might you take pleasure in your trip into the attention-grabbing global of the fourth dimension!
- Chapter zero: what's a Dimension?
- Chapter 1: Dimensions 0 and One
- Chapter 2: the second one Dimension
- Chapter three: 3-dimensional Space
- Chapter four: A Fourth size of Space
- Chapter five: Tesseracts and Hypercubes
- Chapter 6: Hypercube Patterns
- Chapter 7: Planes and Hyperplanes
- Chapter eight: Tesseracts in Perspective
- Chapter nine: Rotations in 4D Space
- Chapter 10: Unfolding a Tesseract
- Chapter eleven: go Sections of a Tesseract
- Chapter 12: dwelling in a 4D House
- Further Reading
- About the Author
Put in your spacesuit, strap in your security harness, swallow your anti-nausea drugs, and revel in this trip right into a fourth measurement of area! 10D, 9D, 8D, 7D, 6D, 5D, 4D, 3D, 2nd, 1D, 0D. Blast off!
By George E. Martin (auth.)
Geometric buildings were a favored a part of arithmetic all through background. the traditional Greeks made the topic an paintings, which was once enriched by way of the medieval Arabs yet which required the algebra of the Renaissance for an intensive figuring out. via coordinate geometry, numerous geometric building instruments may be linked to a number of fields of actual numbers. This e-book is ready those institutions. As laid out in Plato, the sport is performed with a ruler and compass. the 1st bankruptcy is casual and begins from scratch, introducing the entire geometric buildings from highschool which were forgotten or have been by no means obvious. the second one bankruptcy formalizes Plato's online game and examines difficulties from antiquity akin to the impossibility of trisecting an arbitrary attitude. After that, diversifications on Plato's subject are explored: utilizing just a ruler, utilizing just a compass, utilizing toothpicks, utilizing a ruler and dividers, utilizing a marked rule, utilizing a tomahawk, and finishing with a bankruptcy on geometric buildings via paperfolding. the writer writes in an enthralling type and well intersperses background and philosophy in the arithmetic. He hopes that readers will study a bit geometry and a bit algebra whereas having fun with the hassle. this is often as a lot an algebra publication because it is a geometry ebook. because the entire algebra and all of the geometry which are wanted is constructed in the textual content, little or no mathematical historical past is needed to learn this publication. this article has been type established for numerous semesters with a master's point type for secondary teachers.
By Thomas L. Heath
After learning either classics and arithmetic on the collage of Cambridge, Sir Thomas Little Heath (1861-1940) used his time clear of his task as a civil servant to post many works almost about historical arithmetic, either well known and educational. First released in 1926 because the moment version of a 1908 unique, this booklet includes the second one quantity of his three-volume English translation of the 13 books of Euclid's components, protecting Books 3 to 9. This specified textual content can be of price to somebody with an curiosity in Greek geometry and the historical past of arithmetic.
By Ian Tweddle
Most mathematicians' wisdom of Euclid's misplaced paintings on Porisms comes from a truly short and basic description by way of Pappus of Alexandria. whereas Fermat and others made prior makes an attempt to give an explanation for the Porisms, it truly is Robert Simson who's in most cases known because the first individual to accomplish a real perception into the genuine nature of the subject.
In this publication, Ian Tweddle, a known authority on 18th century Scottish arithmetic, provides for the 1st time a whole and obtainable translation of Simson's paintings. in keeping with Simson's early paper of 1723, the treatise, and numerous extracts from Simson's notebooks and correspondence, this booklet offers a desirable perception into the paintings of an often-neglected determine. Supplemented via ancient and mathematical notes and reviews, this publication is a worthwhile addition to the literature for a person with an curiosity in mathematical heritage or geometry.
By Sakai, Takashi
This quantity is an English translation of Sakai's textbook on Riemannian geometry which was once initially written in jap and released in 1992. The author's motive at the back of the unique booklet was once to supply to complicated undergraduate and graduate scholars an advent to fashionable Riemannian geometry which can additionally function a reference. The booklet starts with an evidence of the elemental idea of Riemannian geometry. detailed emphasis is put on understandability and clarity, to lead scholars who're new to this sector. the rest chapters care for a number of themes in Riemannian geometry, with the focus on comparability tools and their purposes.