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Have you ever wondered how to measure your pizza or how much ice cream is in your ice-cream cone? Basic principles of geometry, including measuring two-dimensional and three-dimensional shapes, attributes of various shapes, formulas for finding area and volume, and so much more, are explored through diagrams, photos, and informative and engaging text. Written in a question-and-answer narrative, readers are encouraged to ask questions and guess the...
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Have you ever seen a building that looks like a koala bear, a robot, an elephant, or a pair of pants? This intriguing title teaches readers about skyscrapers that truly stand out! From Beijing to Bangkok, students will learn how to calculate area while reading about the world's most fascinating skyscrapers like the Robot Building and the Elephant Tower. This math reader builds literacy and math content knowledge while introducing students to the concept...
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Translated into many languages, this book was in continuous use as the standard university-level text for a quarter-century, until it was revised and enlarged by the author in 1952. World-renowned writer and researcher Nathan Altshiller-Court (1881–1968) was a professor of mathematics at the University of Oklahoma for more than thirty years. His revised introduction to modern geometry offers today's students the benefits of his many years of teaching...
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Gauss's theory of surfaces is among the purely mathematical achievements inspired by ideas that arose in connection with surveys of the surface of the earth. Long regarded as a masterpiece in content and form, this work features one of the author's most original contributions to mathematics--the discovery that Gauss termed the "Theorema Egregium." It consists of his penetrating definition of the concept of surface curvature and the theorem that the...
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The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory. Unlike most graph theory treatises, this text features complete proofs for almost all...
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In this original text, prolific mathematics author Steven G. Krantz addresses conformal geometry, a subject that has occupied him for four decades and for which he helped to develop some of the modern theory. This book takes readers with a basic grounding in complex variable theory to the forefront of some of the current approaches to the topic. "Along the way," the author notes in his Preface, "the reader will be exposed to some beautiful function...
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To remove the contents of an egg without puncturing its shell or to drink the liquor in a bottle without removing the cork is clearly unthinkable - or is it? Understanding the world of Einstein and curved space requires a logical conception of the fourth dimension. This readable, informative volume provides an excellent introduction to that world, with 22 essays that employ a minimum of mathematics. Originally written for a contest sponsored by Scientific...
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Newly updated accessible study covers parametric and non-parametric surfaces, isothermal parameters, Bernstein's theorem, much more, including such recent developments as new work on Plateau's problem and on isoperimetric inequalities. Clear, comprehensive examination provides profound insights into crucial area of pure mathematics. 1986 edition. Index.
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This book derives from author Nolan R. Wallach's notes for a course on symplectic geometry and Fourier analysis, which he delivered at Rutgers University in 1975 for an audience of graduate students in mathematics and their professors. The monograph is geared toward readers who have taken a basic course in differential manifolds and elementary functional analysis. The first chapters cover certain geometric preliminaries, advancing to discussions of...
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With its coverage of plane, solid, coordinate, vector, and non-Euclidean geometry, this text is suitable for high school, college, and continuing education courses as well as independent study. Each new topic is carefully developed and clarified with many examples. More than 2,000 illustrations help students visualize the problems. Every set of exercises is preceded by numerous examples with detailed solutions. Chapters include a vocabulary list,...
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Elegant and original, this exposition explores the foundations and development of both Euclidean and non-Euclidean geometry, particularly the postulational geometry of planes. Emphasis is placed upon the coordination of affine and projective planes as well as the basic unity of algebra and geometry. Geared toward undergraduate and graduate students, the treatment begins with a brief but engaging sketch of the historical background of Euclidean geometry...
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This study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser known curves.Informative discussions of the line, circle, parabola, ellipse, and hyperbola presuppose only the...
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