Download or read book The Trisectors written by Underwood Dudley and published by American Mathematical Soc.. This book was released on 2019-07-01 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Underwood Dudley is well known for his collection of books on mathematical cranks. Here he offers yet another--angle trisectors. It is impossible to trisect angles with straightedge and compass alone, but many people try and think they have succeeded. This book is about angle trisections and the people who attempt them. According to Dudley: ""Hardly any mathematical training is necessary to read this book. There is a little trigonometry here and there, but it may be safely skipped. There are hardly any equations. There are no exercises and there will be no final examination. The worst victim o.
Download or read book Let s Play Math written by Denise Gaskins and published by Tabletop Academy Press. This book was released on 2012-09-04 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Budget of Trisections written by Underwood Dudley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is impossible to trisect angles with straightedge and compass alone, but many people try and think they have succeeded. This book is about angle trisections and the people who attempt them. Its purposes are to collect many trisections in one place, inform about trisectors, to amuse the reader, and, perhaps most importantly, to reduce the number of trisectors. This book includes detailed information about the personalities of trisectors and their constructions. It can be read by anyone who has taken a high school geometry course.
Download or read book Tales of Impossibility written by David S. Richeson and published by Princeton University Press. This book was released on 2021-11-02 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs—which demonstrated the impossibility of solving them using only a compass and straightedge—depended on and resulted in the growth of mathematics. Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems. Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.
Download or read book A history of Greek mathematics written by Thomas Little Heath and published by Dalcassian Publishing Company. This book was released on 1921-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Euler s Gem written by David S. Richeson and published by Princeton University Press. This book was released on 2019-07-23 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: How a simple equation reshaped mathematics Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.
Download or read book Ruler and Compass written by Andrew Sutton and published by Bloomsbury Publishing USA. This book was released on 2009-11-03 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an introduction to the origins and principles of geometry, describing geometric constructions that can be achieved through the use of rulers and compasses.
Download or read book Geometric Constructions written by George E. Martin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric constructions have been a popular part of mathematics throughout history. The first chapter here is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never learned. The second chapter formalises Plato's game, and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, a compass, toothpicks, a ruler and dividers, a marked rule, or a tomahawk, ending in a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics, teaching a little geometry and a little algebra along the way. This is as much an algebra book as it is a geometry book, yet since all the algebra and geometry needed is developed within the text, very little mathematical background is required. This text has been class tested for several semesters with a master's level class for secondary teachers.
Download or read book Famous Problems of Elementary Geometry written by Felix Klein and published by Cosimo, Inc.. This book was released on 2007-05-01 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This short book, first published in 1897, addresses three geometry puzzles that have been passed down from ancient times. Written for high school students, this book aims to show a younger audience why math should matter and to make the problems found in math intriguing. Klein presents for his readers an investigation of the possibility or impossibility of finding solutions for the following problems in light of mathematics available to him: duplication of the cube trisection of an angle quadrature of the circle Mathematicians and students of the history of math will find this an intriguing work. German mathematician FELIX KLEIN (1849 1925), a great teacher and scientific thinker, significantly advanced the field of mathematical physics and made a number of profound discoveries in the field of geometry. His published works include Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis and Elementary Mathematics from an Advanced Standpoint: Geometry."
Download or read book How Round is Your Circle written by John Bryant and published by Princeton University Press. This book was released on 2008 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'How Round is your Circle?' includes chapters on: hard lines; how to draw a straight line; four-bar variations; building the world's first rules; dividing the circle; falling aprat; follow my leader; all approximations are rational; all a matter of balance; and finding some equilibrium.
Download or read book Textual Studies in Ancient and Medieval Geometry written by W.R. Knorr and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: For textual studies relating to the ancient mathematical corpus the efforts by the Danish philologist, 1. L. Heiberg (1854-1928), are especially significant. Beginning with his doctoral dissertation, Quaestiones Archimedeae (Copen hagen, 1879), Heiberg produced an astonishing series of editions and critical studies that remain the foundation of scholarship on Greek mathematical 4 science. For comprehensiveness and accuracy, his editions are exemplary. In his textual studies, as also in the prolegomena to his editions, he carefully described the extant evidence, organized the manuscripts into stemmata, and drew out the implications for the state of the text. 5 With regard to his Archimedean work, Heiberg sometimes betrayed signs of the philologist's occupational disease - the tendency to rewrite a text deemed on subjective grounds to be unworthy. 6 But he did so less often than his prominent 7 contemporaries, and not as to detract appreciably from the value of his editions. In examining textual questions bearing on the Archimedean corpus, he attempted to exploit as much as possible evidence from the ancient commentators, and in some instances from the medieval translations. It is here that opportunities abound for new work, extending, and in some instances superseding, Heiberg's findings. For at his time the availability of the medieval materials was limited. In recent years Marshall Clagett has completed a mammoth critical edition of the medieval Latin tradition of Archimedes,8 while the bibliographical instruments for the Arabic tradition are in good order thanks to the work of Fuat Sezgin.
Download or read book The Wonder Book of Geometry written by David Acheson and published by Oxford University Press. This book was released on 2020-10-22 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can we be sure that Pythagoras's theorem is really true? Why is the 'angle in a semicircle' always 90 degrees? And how can tangents help determine the speed of a bullet? David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at its best. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.
Download or read book Elementary Geometry from an Advanced Standpoint written by Edwin E. Moise and published by Addison Wesley. This book was released on 1990 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students can rely on Moise's clear and thorough presentation of basic geometry theorems. The author assumes that students have no previous knowledge of the subject and presents the basics of geometry from the ground up. This comprehensive approach gives instructors flexibility in teaching. For example, an advanced class may progress rapidly through Chapters 1-7 and devote most of its time to the material presented in Chapters 8, 10, 14, 19, and 20. Similarly, a less advanced class may go carefully through Chapters 1-7, and omit some of the more difficult chapters, such as 20 and 24.
Download or read book Excursions in Geometry written by Charles Stanley Ogilvy and published by Courier Corporation. This book was released on 1990-01-01 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: A straightedge, compass, and a little thought are all that's needed to discover the intellectual excitement of geometry. Harmonic division and Apollonian circles, inversive geometry, hexlet, Golden Section, more. 132 illustrations.
Download or read book Single Digits written by Marc Chamberland and published by Princeton University Press. This book was released on 2017-05-30 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The numbers one through nine have remarkable mathematical properties and characteristics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? Are there really "six degrees of separation" between all pairs of people? And how can any map need only four colors to ensure that no regions of the same color touch? In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics."--Jacket.
Download or read book Famous Problems of Geometry and How to Solve Them written by Benjamin Bold and published by Courier Corporation. This book was released on 2012-05-11 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
