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Projective Geometry and Projective Metrics

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The basic results and methods of projective and non-Euclidean geometry are indispensable for the geometer, and this book--different in content, methods, and point of view from traditional texts--attempts to emphasize that fact. Results of special theorems are discussed in detail only when they are needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity.Topics include the projective plane, polarities and conic sections, affine geometry, projective metrics, and non-Euclidean and spatial geometry. Numerous figures appear throughout the text, which concludes with a bibliography and index.

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This sumptuous edition offers all 100 full-color plates from Owen Jones's definitive presentation of Chinese ornamentation and design, one of the most beautiful books on the decorative arts ever published. Now, over a centruy after its first publication, this remarkable work continues to provide an excellent, copyright-free source of authentic Chinese design and motifs. During the vast political tumult in China in the 19th century, many of the most exquisite examples of native art from the Ming, Ch'ing and earlier dynasties were spirited out of the country and sold into Western collections. One of the most spectacular of these assemblages was housed at London's South Kensington Museum (today The Victoria and Albert Museum). In the 1860s, the noted English designer and architect Owen Jones studed this collection in depth, particularly the wealth of superb examples of porcelain and cloisonne. He then meticulously rendered many of the most intriguing and beautiful designs in full color. These were published in his celebrated book, Examples of Chinese Ornament Selected from Objects in the South Kensington Museum and Other Collections (1867).This volume offers painstaking reproductions of all one hundred original color plates from that work, which delighted the art world of the time and exerted a profound influence on the subsequent history of Western design. Now that visual inspiration is once again available to artists, illustrators, designers, and craftspeople in this inexpensive high-quality edition. Moreover, any lover of fine art can enjoy the book as a splendid tribute to the glories of Chinese designat a price far less than those commanded by extremely rare surviving copies of Jones's original work.

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An ideal text for undergraduate courses in projective geometry, this volume begins on familiar ground. It starts by employing the leading methods of projective geometry as an extension of high school-level studies of geometry and algebra, and proceeds to more advanced topics with an axiomatic approach.An introductory chapter leads to discussions of projective geometry's axiomatic foundations: establishing coordinates in a plane; relations between the basic theorems; higher-dimensional space; and conics. Additional topics include coordinate systems and linear transformations; an abstract consideration of coordinate systems; an analytical treatment of conic sections; coordinates on a conic; pairs of conics; quadric surfaces; and the Jordan canonical form. Numerous figures illuminate the text.

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Full-Color Picture Sourcebook of Historic Ornament

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All 120 Plates from "L'Ornement Polychrome," Series II

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The present Dover edition contains all 120 plates from Racinet's Series II, with brief new English captions that summarize the French text. The copious material, ranging from Ireland to China and from ancient Egypt to the late nineteenth century, is derived from a wide range of arts and crafts including architecture, painting, woodwork, metalwork, ceramics, and textiles. Racinet's purpose in publishing these masterpieces of decoration was the encouragement and improvement of the arts of his own day, not only the so-called fine arts but also the commercial arts involved in the designing and marketing of manufactured goods. Dover's reissue of the plates, recognizing their perennial value and appeal, naturally is meant to serve the same purpose. Racinet's breadth of insight and catholicity of taste, truly enlightened for his day, give his selection a welcome variety and a consistently high standard of excellence; while the consummate skill of his artistic workers and of his printer-publisher, the celebrated Firmin-Didot Company, make these plates true works of art in their own right. Racinet's color plates were prepared on the basis of existing works of art by a number of capable commercial artists, identified in the original edition at the lower left-hand corner of each plate. These artists are represented in Series II of L'Ornement Polychrome: Bauer, Benard, Brandin, Charpentier, Chataignon, Cottelot, Daumont, Debenais, Dreus, Durin, Gaulard, Gautier, Guesnu, Lemoine, Lestel, Manoury, Mathieu, Mauler, Meheux, Nordmann, Picard, Schmidt, Spiegel, Taillefer, and Waret.

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Fantastic Gothic and Renaissance Ornament

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Dancing beasts of myth and legend, thick foliage that appears to live and breathe, reclining figures engulfed by symbols of fate  this magnificent compendium of 15th- and 18th-century embellishments offers up a dizzying array of Gothic and Renaissance designs steeped in religion and fantasy. A marvel of art history, 127 exquisitely rendered black-and-white illustrations will thrill students and art aficionados, and serve as a rich source of inspiration for anyone working in the fine or applied arts.

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The greatest writer of French classic comedy, the 17th-century playwright Moliere was one of the most brilliant satirists in the history of literature. His keen observations and barbed wit deflated the pretensions of society in his day and focused a brilliant light on the universal frailties of humanity.The Imaginary Invalid, one of Moliere's funniest and most incisive satires, is also among the most performed worldwide and perennially studied in world literature courses. In this entertaining gem, a hypochondriac, victimized by two pompous doctors, tests his daughter's loyalty and discovers the greed and contempt of his scheming wife.

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Much-studied and frequently performed, these comedies by the great Elizabethan playwright Ben Jonson satirize the greed, mendacity, gullibility, and pretension of seventeenth-century London society. Both plays abound in colorful characters, ingenious plotting, biting wit, and sharp insight into human nature. In Volpone (1605), a crafty rich man attempts to augment his wealth by feigning a mortal illness. His wealthy neighbors, spying the opportunity for an inheritance, vie with each other in courting the dying mans favor. The Alchemist (1610) comprises a likewise avaricious cast, headed by a butler and prostitute who join forces with a swindler claiming to possess the philosopher's stone. The trio hosts a parade of eager victims whose hypocrisy and greed place them on a moral footing similar to that of the tricksters. Both plays offer sparkling examples of their author's novel approach to satire and his distinctive blend of savagery, humor, moralism, and a powerful sense of the absurd.

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11 carefully chosen, highly readable stories  among the earliest literature known to Western man  provide a glimpse into the lives and culture of ancient Egyptians. Includes "The Scorpions of Isis," "The Princess and the Demon," "The Name of Ra," "The Regions of Night and Thick Darkness," and more.

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Victorian Sourcebook of Medieval Decoration

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Compiled by two noted British architects and designers, this magnificent volume was intended to provide Victorian artists and crafters with a rich source of ornamentation adapted from the decoration of medieval buildings.Meticulously reproduced motifs from rare 1882 edition, this volume contains all the original 166 full-color designs as well as the informative introduction and notes on the original plates. Among the designs are elaborate and richly colored diaper patterns, medallions for ornamental devices, pillars and arch moldings, bands and borders, floral and foliated designs, alphabets, illuminated initials, and much more. As in Victorian England, today's artists, designers, and crafters will find these beautiful royalty-free designs ideal for visual inspiration or immediate practical use. Students, art historians, and lovers of fine design will also welcome this collection for its splendid examples of medieval artistry.

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The Victorians loved their flowers, and from a stunning nineteenth-century collection of floral motifs comes this garden of decorative designs. Exquisitely detailed and stylistically rare, its illustrations feature lush blossoms and plants surrounded by design elements of the most magnificent order.These 72 pages offer a wealth of images for a virtually unlimited array of applications. Perfect for enhancing greeting cards, newsletters, and websites, these gorgeous black-and-white patterns also offer inspiration for needlework and other craft projects.

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A Pictorial Archive for Artists and Designers

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Heraldry had its origin in the decorative shields used in Western Europe in the twelfth century. Today the varied and colorful designs that have developed over the centuries carry a rich aura of medieval romance that can enhance any number of artistic and design projects.For this volume, Carol Belanger Grafton has selected 1,047 authentic heraldic designs and motifs from The Art of Heraldry, a classic study by Arthur Charles Fox-Davies (18711928), an English barrister and foremost authority on the subject. Dating from the fourteenth to the twentieth centuries, the illustrations include 393 full-color and 654 black-and-white designs: arms of individuals, among them such notables as Edward the Black Prince, John Milton, and Maximilian I; arms of institutions, corporations, guilds, towns, and cities; heraldic windows; examples of heraldic lions, eagles, and dragons; banners and crests; and more.These designs represent a superb source of authentic royalty-free images that will give aristocratic flair to book and magazine illustrations, advertisements, newsletters, and other graphic projects. This volume is also a valuable visual reference for those interested in genealogy.

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A comprehensive approach to qualitative problems in intrinsic differential geometry, this text for upper-level undergraduates and graduate students emphasizes cases in which geodesics possess only local uniqueness properties--and consequently, the relations to the foundations of geometry are decidedly less relevant, and Finsler spaces become the principal subject.This direct approach has produced many new results and has materially generalized many known phenomena. Author Herbert Busemann begins with an explanation of the basic concepts, including compact metric spaces, convergence of point sets, motion and isometry, segments, and geodesics. Subsequent topics include Desarguesian spaces, with discussions of Riemann and Finsler spaces and Beltrami's theorem; perpendiculars and parallels, with examinations of higher-dimensional Minkowskian geometry and the Minkowski plane; and covering spaces, including locally isometric space, the universal covering space, fundamental sets, free homotopy and closed geodesics, and transitive geodesics on surfaces of higher genus. Concluding chapters explore the influence of the sign of the curvature on the geodesics, and homogenous spaces, including those with flat bisectors.

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General Investigations of Curved Surfaces

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Edited with an Introduction and Notes by Peter Pesic

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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 "Gauss curvature" is invariant under arbitrary isometric deformation of a curved surface. The profound effects of these concepts were soon generalized by Bernhard Riemann, and subsequent development included the important role of the Gauss-Riemann concept of curvature in modern relativity theory.This edition of Gauss's classic work features a new introduction, bibliography, and notes by science historian Peter Pesic. In addition, an informative appendix offers historical background.

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Karl Friedrich Gauss, Peter Pesic, Adam Hiltebeitel, James Morehead

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This text for advanced undergraduate students is both an introduction to algebraic geometry and a bridge between its two parts  the analytical-topological and the algebraic. Because of its extensive use of formal power series (power series without convergency), the treatment will appeal to readers conversant with analysis but less familiar with the formidable techniques of modern algebra. The book opens with an overview of the results required from algebra and proceeds to the fundamental concepts of the general theory of algebraic varieties: general point, dimension, function field, rational transformations, and correspondences. A concentrated chapter on formal power series with applications to algebraic varieties follows. An extensive survey of algebraic curves includes places, linear series, abelian differentials, and algebraic correspondences. The text concludes with an examination of systems of curves on a surface.

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Simple, easy-to-follow instructions and 105 figure drawings show how to execute more than 35 amazing card tricks using such ordinary items as a handkerchief, notepaper, piece of string, candle, and a deck of cards. Beginners will soon be performing remarkable feats iincluding The Thirty Card Trick, A False Riffle Shuffle, and more.

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When party guests request a few tricks, be prepared. Ask for a coin, and perform some of the tricks in this book. Because you will not have been aided by special stage apparatus, the results will be all the more astonishing. As tricks with coins are so readily improvised, they are among the most impressive forms of legerdemain.This book is the most complete treatise ever written on sleight-of-hand coin conjuring. Celebrated magician J. B. Bobo has gathered here the best and most useful of all coin tricks  not only his own, but those of some four dozen notable prestidigitators, including such greats as Robert-Houdin, Professer Hoffman, and  the greatest of all coin conjurers  T. Nelson Downs.All the tested, traditional methods of coin magic are here. Bobo has added to these the best of the modern innovations, while eliminating all of the out-of-date and impractical sleights of his sources. You will learn all about palms, holds, flips, switches, change-over, steals, cuffing, sleeving, and other sleight-of-hand techniques; coin tricks requiring special devices are also included. The author guides how systematically from basic techniques, concealments, and vanishes, through integrated tricks, to complete routine acts (18 in all). His clear explanations are splendidly complemented by 510 of Nelson C. Hahne's crisp illustrations.Sleight-of-hand magic has consistently earned the respect of professional magicians. If you are yet an amateur, this easy-to-follow manual  together with regular practice  is the surest route to professional-level competence. For professionals, this volume is a convenient encyclopedic reference that gathers in one place all the best coin magic from antiquity to modern times.

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The Early Mathematical Manuscripts of Leibniz

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The manuscripts and correspondence of Leibniz possess a special interest: they are invaluable as aids to the study of their author's part in the invention and development of the infinitesimal calculus. In addition, the main ideas behind Leibniz's philosophical theories lay here, in his mathematical work.This volume consists of two sections. The first part features Leibniz's own accounts of his work, and the second section comprises critical and historical notes and essays. An informative Introduction leads to the "postscript" to Leibniz's 1703 letter to James Bernoulli, his "Historia et Origio Calculi Differentialis," and manuscripts of the period 1673-77. Essays by the distinguished scholar C. I. Gerhardt follow--Leibniz in London and Leibniz and Pascal, along with additional letters and manuscripts by Leibniz.

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Set theory permeates much of contemporary mathematical thought. This text for undergraduates offers a natural introduction, developing the subject through observations of the physical world. Its progressive development leads from concrete finite sets to cardinal numbers, infinite cardinals, and ordinals.Although set theory begins in the intuitive and the concrete, it ascends to a very high degree of abstraction. All that is necessary to its grasp, declares author Joseph Breuer, is patience. Breuer illustrates the grounding of finite sets in arithmetic, permutations, and combinations, which provides the terminology and symbolism for further study. Discussions of general theory lead to a study of ordered sets, concluding with a look at the paradoxes of set theory and the nature of formalism and intuitionalism. Answers to exercises incorporated throughout the text appear at the end, along with an appendix featuring glossaries and other helpful information.

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This single-volume compilation of two books explores the construction of geometric proofs. In addition to offering useful criteria for determining correctness, it presents examples of faulty proofs that illustrate common errors. High-school geometry is the sole prerequisite.Proof in Geometry, the first in this two-part compilation, discusses the construction of geometric proofs and presents criteria useful for determining whether a proof is logically correct and whether it actually constitutes proof. It features sample invalid proofs, in which the errors are explained and corrected.Mistakes in Geometric Proofs, the second book in this compilation, consists chiefly of examples of faulty proofs. Some illustrate mistakes in reasoning students might be likely to make, and others are classic sophisms. Chapters 1 and 3 present the faulty proofs, and chapters 2 and 4 offer comprehensive analyses of the errors.

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Harmonic Analysis and the Theory of Probability

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Nineteenth-century studies of harmonic analysis were closely linked with the work of Joseph Fourier on the theory of heat and with that of P. S. Laplace on probability. During the 1920s, the Fourier transform developed into one of the most effective tools of modern probabilistic research; conversely, the demands of the probability theory stimulated further research into harmonic analysis.Mathematician Salomon Bochner wrote a pair of landmark books on the subject in the 1930s and 40s. In this volume, originally published in 1955, he adopts a more probabilistic view and emphasizes stochastic processes and the interchange of stimuli between probability and analysis. Non-probabilistic topics include Fourier series and integrals in many variables; the Bochner integral; the transforms of Plancherel, Laplace, Poisson, and Mellin; applications to boundary value problems, to Dirichlet series, and to Bessel functions; and the theory of completely monotone functions.The primary significance of this text lies in the last two chapters, which offer a systematic presentation of an original concept developed by the author and partly by LeCam: Bochner's characteristic functional, a Fourier transform on a Euclidean-like space of infinitely many dimensions. The characteristic functional plays a role in stochastic processes similar to its relationship with numerical random variables, and thus constitutes an important part of progress in the theory of stochastic processes.