If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.
Delve into the development of modern mathematics and match wits with Euclid, Newton, Descartes, and others. Each chapter explores an individual type of challenge, with commentary and practice problems. Solutions.
An introduction to geometry without measurements.
Craig Barton is one of the world's most respected teachers of mathematics. In his remarkable new book, he explains how he has delved into the world of academic research and emerged with a range of simple, practical, effective strategies to save time and energy and have a positive impact on the long-term learning and enjoyment of students.
The classic Heath translation, in a completely new layout with plenty of space and generous margins. An affordable but sturdy sewn hardcover student and teacher edition in one volume, with minimal notes and a new index/glossary.
This is the ultimate master class in modern physics. World-class physicist and father of string theory Leonard Susskind and citizen-scientist George Hrabovsky combine forces in a primer that teaches the skills you need to do physics yourself. Combining crystal-clear explanations of the laws of the universe with basic exercises (including essential equations and maths), the authors cover the minimum that readers should master. They introduce the key concepts of modern physics, from classical mechanics to general relativity to quantum theory, and provide a practical toolkit that you won't find in any other popular science book.
Mathematical Time Capsules offers teachers historical modules for immediate use in the mathematics classroom. Readers will find articles and activities from mathematics history that enhance the learning of topics covered in the undergraduate or secondary mathematics curricula. Each capsule presents at least one topic or a historical thread that can be used throughout a course. The capsules were written by experienced practitioners to provide teachers with historical background and classroom activities designed for immediate use in the classroom, along with further references and resources on the chapter subject. --Publisher description.
Signs and wonders: A fantastic journey through the history of esoteric lore The Hermetic Museumtakes readers on a magical mystery tour spanning an arc from the medieval cosmogram and images of Christian mysticism, through the fascinating world of alchemy to the art of the Romantic era. The enigmatic hieroglyphs of cabalists, Rosicrucians, and freemasons are shown to be closely linked with the early scientific illustrations in the fields of medicine, chemistry, optics, and color theory. Even for those with no knowledge of the fascinating history of alchemy, this book is a delight to explore. Each richly illustrated chapter begins with an introduction and quotes from alchemists by specialist Alexander Roob. The roots of surrealism and many other more recent artistic movements can be found in this treasure trove. About the Series: Bibliotheca Universalis Compact cultural companions celebrating the eclectic TASCHEN universe at an unbeatable, democratic price!Since we started our work as cultural archaeologists in 1980, the name TASCHEN has become synonymous with accessible, open-minded publishing.Bibliotheca Universalisbrings together nearly 100 of our all-time favorite titles in a neat new format so you can curate your own affordable library of art, anthropology, and aphrodisia.Bookworm s delight never bore, always excite! "
This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis—finding the “right axioms” to prove fundamental theorems—and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the “right axiom” to prove it. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.
"An enchanting history of Japanese geometry--of a time and place where 'geometers did not cede place to poets.' This intersection of science and culture, of the mathematical, the artistic, and the spiritual, is packed, like circles within circles, with rewarding Aha! epiphanies that drive a mathematician's curiosity."--Siobhan Roberts, author of "King of Infinite Space" "Teachers will welcome this remarkable collection of mathematical problems, history, and art, which will enrich their curriculum and promote both logical thinking and critical evaluation. It is especially important that we maintain an interest in geometry, which needs, and for once gets, more than its share."--Richard Guy, coauthor of "The Book of Numbers" "This remarkable book provides a novel insight into the Japanese mathematics of the past few hundred years. It is fascinating to see the difference in mathematical style from that which we are used to in the Western world, but the book also elegantly illustrates the cross-cultural Platonic nature and profound beauty of mathematics itself."--Roger Penrose, author of "The Road to Reality" "A significant contribution to the history of mathematics. The wealth of mathematical problems--from the very simple to quite complex ones--will keep the interested reader busy for years. And the beautiful illustrations make this book a work of art as much as of science. Destined to become a classic!"--Eli Maor, author of "The Pythagorean Theorem: A 4,000-Year History" "A pleasure to read. "Sacred Mathematics" brings to light the unique style and character of geometry in the traditional Japanese sources--in particular the "sangaku" problems. These problems range from trivial to utterly devilish. I found myself captivated by them, and regularly astounded by the ingenuity and sophistication of many of the traditional solutions."--Glen Van Brummelen, coeditor of "Mathematics and the Historian's Craft"
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
This book examines the textual, social, cultural, practical and institutional environments to which the expression “teaching and learning contexts” refers. It reflects on the extent to which studying such environments helps us to better understand ancient or modern sources, and how notions of “teaching” and “learning” are to be understood. Tackling two problems: the first, is that of certain sources of scientific knowledge being studied without taking into account the various “contexts” of transmission that gave this knowledge a long-lasting meaning. The second is that other sources are related to teaching and learning activities, but without being too precise and demonstrative about the existence and nature of this “teaching context”. In other words, this book makes clear what is meant by “context” and highlights the complexity of the practice hidden by the words “teaching” and “learning”. Divided into three parts, the book makes accessible teaching and learning situations, presents comparatist approaches, and emphasizes the notion of teaching as projects embedded in coherent treatises or productions.
Why should mathematics, the purest of sciences, have a history? Medieval mathematicians took little interest in the history of their discipline. Yet in the Renaissance the history of mathematics flourished. This book explores how Renaissance scholars recovered and reconstructed the origins of mathematics by tracing its invention in prehistoric Antiquity, its development by the Greeks, and its transmission to modern Europe via the works of Euclid, Theon and Proclus. The principal architects of this story -- the French philosopher and University of Paris reformer Peter Ramus, and his critic, the young Oxford astronomy lecturer Henry Savile – worked out diametrically opposed models for the development of the mathematical arts, models of historical progress and decline which mirrored each scholar’s larger convictions about the nature of mathematical thinking, the purpose of the modern university, and the potential of the human mind. In their hands, the obscure story of mathematical history became a site of contention over some of the most pressing philosophical and pedagogical debates of the sixteenth century.
Botanical beauty: Basilius Besler's complete Hortus Eystettensis of 1613 A magnificent pictorial document of the flowers grown in the greatest German garden of its time, the Hortus Eystettensis is in a class of its own when it comes to the range of flowers engraved. First published in 1613, the 367 copperplate engravings by Basilius Besler (1561-1629) capture the spectacular diversity of the palatial gardens of Prince-Bishop Johann Konrad von Gemmingen (1593/95-1612) in Eichstätt, Bavaria, Germany. The meticulous illustrations are organized according to the four seasons, and, following the classification system used today, show plants belonging to a total of 90 families and covering 340 genera. The whole collection is regarded as one of the finest treasures of botanical literature, described by Carl Linnaeus, the legendary 18th-century botanist and zoologist, as an "incomparable work". Besler's pictorial catalog long outlived the gardens, which were destroyed in 1634 by invading Swedish troops. In auction, the asking price for a first-edition copy of Hortus Eystettensis is now more than half a million dollars. With this edition, TASCHEN opens up the garden to a much wider audience: A rich and beautiful record, destined to keep the garden's beauty in bloom. About the Series: Bibliotheca Universalis -- Compact cultural companions celebrating the eclectic TASCHEN universe at an unbeatable, democratic price! Since we started our work as cultural archaeologists in 1980, the name TASCHEN has become synonymous with accessible, open-minded publishing. Bibliotheca Universalis brings together nearly 100 of our all-time favorite titles in a neat new format so you can curate your own affordable library of art, anthropology, and aphrodisia. Bookworm's delight -- never bore, always excite!
Euclid presents the essential of mathematics in a manner which has set a high standard for more than 2000 years. This book, an explanation of the nature of mathematics from its most important early source, is for all lovers of mathematics with a solid background in high school geometry, whether they be students or university professors.
TASCHEN's 25th anniversary - Special edition! New design, new low price! The most famous botanical record ever committed to paper: Basilius Besler's complete Book of Plants of 1613 A magnificent pictorial document of the flowers grown in the greatest German garden of its time, the Book of Plants is in a class of its own when it comes to the variety and range of flowers engraved. Working under Basilius Besler, a team of at least ten engravers worked on this massive project, translating in situ and specimen drawings faithfully to copper plates. Nearly four hundred years old, the book has survived though the gardens did not; they were destroyed by invading Swedish troops in 1634. However, in 1998 a reconstruction of the original garden opened to the public in Eichst'tt. This facsimile's reproductions - structured by seasons - are taken from a hand-painted edition, one of only a few still extant. In auction, the asking price for a first edition copy is half a million dollars. You can now enjoy its unique qualities for somewhat less.
PREFACE. THE Author of this very practical treatise on Scotch Loch - Fishing desires clearly that it may be of use to all who had it. He does not pretend to have written anything new, but to have attempted to put what he has to say in as readable a form as possible. Everything in the way of the history and habits of fish has been studiously avoided, and technicalities have been used as sparingly as possible. The writing of this book has afforded him pleasure in his leisure moments, and that pleasure would be much increased if he knew that the perusal of it would create any bond of sympathy between himself and the angling community in general. This section is interleaved with blank shects for the readers notes. The Author need hardly say that any suggestions addressed to the case of the publishers, will meet with consideration in a future edition. We do not pretend to write or enlarge upon a new subject. Much has been said and written-and well said and written too on the art of fishing but loch-fishing has been rather looked upon as a second-rate performance, and to dispel this idea is one of the objects for which this present treatise has been written. Far be it from us to say anything against fishing, lawfully practised in any form but many pent up in our large towns will bear us out when me say that, on the whole, a days loch-fishing is the most convenient. One great matter is, that the loch-fisher is depend- ent on nothing but enough wind to curl the water, -and on a large loch it is very seldom that a dead calm prevails all day, -and can make his arrangements for a day, weeks beforehand whereas the stream- fisher is dependent for a good take on the state of the water and however pleasant and easy it may be for one living near the banks of a good trout stream or river, it is quite another matter to arrange for a days river-fishing, if one is looking forward to a holiday at a date some weeks ahead. Providence may favour the expectant angler with a good day, and the water in order but experience has taught most of us that the good days are in the minority, and that, as is the case with our rapid running streams, -such as many of our northern streams are, -the water is either too large or too small, unless, as previously remarked, you live near at hand, and can catch it at its best. A common belief in regard to loch-fishing is, that the tyro and the experienced angler have nearly the same chance in fishing, -the one from the stern and the other from the bow of the same boat. Of all the absurd beliefs as to loch-fishing, this is one of the most absurd. Try it. Give the tyro either end of the boat he likes give him a cast of ally flies he may fancy, or even a cast similar to those which a crack may be using and if he catches one for every three the other has, he may consider himself very lucky. Of course there are lochs where the fish are not abundant, and a beginner may come across as many as an older fisher but we speak of lochs where there are fish to be caught, and where each has a fair chance. Again, it is said that the boatman has as much to do with catching trout in a loch as the angler. Well, we dont deny that. In an untried loch it is necessary to have the guidance of a good boatman but the same argument holds good as to stream-fishing...