Download or read book Trigonometry Geometry and the Conception of Space written by Paul M. Tokorcheck and published by . This book was released on 2015-08-07 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Trigonometry, Geometry, and the Conception of Space is primarily a textbook for students of architecture, design, or any other subject that requires a strong, practical understanding of measurement. Topics that are traditionally included for future calculus students have been replaced with a study of three-dimensional space and geometry. The first portion of the book focuses on pure trigonometry: sets and numbers, the six trigonometric functions and their inverses, and applications. The second portion covers more geometric topics like cylindrical and spherical coordinate systems, conic sections, and quadric surfaces. The material emphasizes alternative ways to describe points in space and how to transfer between them. Written for highly visual courses exploring three-dimensional space and the objects that lie within it, Trigonometry, Geometry, and the Conception of Space offers fresh, modern instruction for classes in architecture, graphic design, and mathematics. Paul Tokorcheck earned his Ph.D. in mathematics at UC Santa Cruz, with research interests in group representations, number theory, and Lie theory. He is now a lecturer with the Department of Mathematics at Iowa State University. Apart from mathematics, Dr. Tokorcheck's life journey has taken him through a variety of jobs, from cooking in award-winning kitchens of California, to teaching high school in northern Ghana, to resettling refugees from the civil wars in Liberia and Sierra Leone."
Download or read book The Theory of the Imaginary in Geometry written by J. L. S. Hatton and published by CreateSpace. This book was released on 2015-01-16 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface. THE position of any real point in space may be determined by eans of three real coordinates, and any three real quantities may be regarded as determining the position of such a point. In Geometry as in other branches of Pure Mathematics the question naturally arises, whether the quantities concerned need necessarily be real. What, it may be asked, is the nature of the Geometry in which the coordinates of any point may be complex quantities of the form x + ix', y + iy' , z + iz'? Such a Geometry contains as a particular case the Geometry of real points. From it the Geometry of real points may be deduced (a) by regarding x', y', z' as zero, (b) by regarding x, y, z as zero, or (c) by considering only those points, the coordinates of which are real multiples of the same complex quantity a+ib. The relationship of the more generalised conception of Geometry and of space to the particular case of real Geometry is of importance, as points, whose determining elements are complex quantities, arise both in coordinate and in projective Geometry. In this book an attempt has been made to work out and determine this relationship. Either of two methods might have been adopted. It would have been possible to lay down certain axioms and premises and to have developed a general theory therefrom. This has been done by other authors. The alternative method, which has been employed here, is to add to the axioms of real Geometry certain additional assumptions. From these, by means of the methods and principles of real Geometry, an extension of the existing ideas and conception of Geometry can be obtained. In this way the reader is able to approach the simpler and more concrete theorems in the first instance, and step by step the well-known theorems are extended and generalised. A conception of the imaginary is thus gradually built up and the relationship between the imaginary and the real is exemplified and developed. The theory as here set forth may be regarded from the analytical point of view as an exposition of the oft quoted but seldom explained "Principle of Continuity." The fundamental definition of Imaginary points is that given by Dr Karl v. Staudt in his Beiträge zur Geometrie der Lage; Nuremberg, 1856 and 1860. The idea of (a, beta) figures, independently evolved by the author, is due to J. V. Poncelet, who published it in his Traité des Propriétés Projectives des Figures in 1822. The matter contained in four or five pages of Chapter II is taken from the lectures delivered by the late Professor Esson, F.R.S., Savilian Professor of Geometry in the University of Oxford, and may be partly traced to the writings of v. Staudt. For the remainder of the book the author must take the responsibility. Inaccuracies and inconsistencies may have crept in, but long experience has taught him that these will be found to be due to his own deficiencies and not to fundamental defects in the theory. Those who approach the subject with an open mind will, it is believed, find in these pages a consistent and natural theory of the imaginary. Many problems however still require to be worked out and the subject offers a wide field for further investigations.
Download or read book The Theory of the Imaginary in Geometry written by J L S Hatton and published by . This book was released on 2019-11-20 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: THE position of any real point in space may be determined by eans of three real coordinates, and any three real quantities may be regarded as determining the position of such a point. In Geometry as in other branches of Pure Mathematics the question naturally arises, whether the quantities concerned need necessarily be real. What, it may be asked, is the nature of the Geometry in which the coordinates of any point may be complex quantities of the form x + ix', y + iy', z + iz'? Such a Geometry contains as a particular case the Geometry of real points. From it the Geometry of real points may be deduced (a) by regarding x', y', z' as zero, (b) by regarding x, y, z as zero, or (c) by considering only those points, the coordinates of which are real multiples of the same complex quantity a+ib. The relationship of the more generalised conception of Geometry and of space to the particular case of real Geometry is of importance, as points, whose determining elements are complex quantities, arise both in coordinate and in projective Geometry. In this book an attempt has been made to work out and determine this relationship. Either of two methods might have been adopted. It would have been possible to lay down certain axioms and premises and to have developed a general theory therefrom. This has been done by other authors. The alternative method, which has been employed here, is to add to the axioms of real Geometry certain additional assumptions. From these, by means of the methods and principles of real Geometry, an extension of the existing ideas and conception of Geometry can be obtained. In this way the reader is able to approach the simpler and more concrete theorems in the first instance, and step by step the well-known theorems are extended and generalised. A conception of the imaginary is thus gradually built up and the relationship between the imaginary and the real is exemplified and developed. The theory as here set forth may be regarded from the analytical point of view as an exposition of the oft quoted but seldom explained " Principle of Continuity." The fundamental definition of Imaginary points is that given by Dr Karl v. Staudt in his Beiträge zur Geometrie der Lage; Nuremberg, 1856 and 1860. The idea of (α, β) figures, independently evolved by the author, is due to J. V. Poncelet, who published it in his Traité des Propriétés Projectives des Figures in 1822. The matter contained in four or five pages of Chapter II is taken from the lectures delivered by the late Professor Esson, F.R.S., Savilian Professor of Geometry in the University of Oxford, and may be partly .traced to the writings of v. Staudt. For the remainder of the book the author must take the responsibility. Inaccuracies and inconsistencies may have crept in, but long experience has taught him that these will be found to be due to his own deficiencies and not to fundamental defects in the theory. Those who approach the subject with an open mind will, it is believed, find in these pages a consistent and natural theory of the imaginary. Many problems however still require to be worked out and the subject offers a wide field for further investigations.
Download or read book A Mathematical Space Odyssey written by Claudi Alsina and published by The Mathematical Association of America. This book was released on 2015-08-21 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solid geometry is the traditional name for what we call today the geometry of three-dimensional Euclidean space. Courses in solid geometry have largely disappeared from American high schools and colleges. The authors are convinced that a mathematical exploration of three-dimensional geometry merits some attention in today’s curriculum. A Mathematical Space Odyssey: Solid Geometry in the 21st Century is devoted to presenting techniques for proving a variety of mathematical results in three-dimensional space, techniques that may improve one’s ability to think visually. Special attention is given to the classical icons of solid geometry (prisms, pyramids, platonic solids, cones, cylinders, and spheres) and many new and classical results: Cavalieri’s principle, Commandino’s theorem, de Gua’s theorem, Prince Rupert’s cube, the Menger sponge, the Schwarz lantern, Euler’s rotation theorem, the Loomis-Whitney inequality, Pythagorean theorems in three dimensions, etc. The authors devote a chapter to each of the following basic techniques for exploring space and proving theorems: enumeration, representation, dissection, plane sections, intersection, iteration, motion, projection, and folding and unfolding. In addition to many figures illustrating theorems and their proofs, a selection of photographs of three-dimensional works of art and architecture are included. Each chapter includes a selection of Challenges for the reader to explore further properties and applications. It concludes with solutions to all the Challenges in the book, references, and a complete index. Readers should be familiar with high school algebra, plane and analytic geometry, and trigonometry. While brief appearances of calculus do occur, no knowledge of calculus is necessary to enjoy this book.
Download or read book Advanced Trigonometry written by C. V. Durell and published by Courier Corporation. This book was released on 2003-11-19 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a welcome resource for teachers seeking an undergraduate text on advanced trigonometry. Ideal for self-study, this book offers a variety of topics with problems and answers. 1930 edition. Includes 79 figures.
Download or read book Dialogue and Boundary Learning written by Peter Neville Rule and published by Springer. This book was released on 2015-12-01 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an increasingly monologic world of war, exploitation and fear of the other , dialogue within and between humans, and with the world around us, is critical to a humane future. This book explores dialogue and learning in theory, practice and praxis across a spectrum of lifelong education contexts. It develops a philosophical basis by examining the lives, works and dialogic traditions of four key thinkers: Socrates, Martin Buber, Mikhail Bakhtin and Paulo Freire. It then examines dialogue and learning in contexts ranging from early childhood development to adult, community and higher education. In doing so, it develops and illustrates the innovative concepts of dialogic space, boundary learning and diacognition. It has a specific focus on learners and learning in contexts of oppression and marginality, and with a view to personal and social emancipation. It is located in an African context, specifically South Africa, although its resonance is both local and global. The book marks an innovative contribution to our understanding of dialogue and learning, framed by the great dialogic traditions of the past, and is a dialogical provocation to the ongoing generation of praxis. This book is valuable for grounding lifelong learning experiences within an African context. It underlines the complexities involved in carrying out authentic dialogue at different stages of education in Africa throughout the lifespan, exploring cases of border crossing and boundary maintenance. Peter Mayo, University of Malta and Series Editor of the International Issues in Adult Education Series
Download or read book The Question of Being in Western and African Analytic Metaphysics written by Grivas Muchineripi Kayange and published by Springer Nature. This book was released on 2021-05-04 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim of this book is to discuss fundamental developments on the question of being in Western and African philosophy using analytic metaphysics as a framework. It starts with the two orthodox responses to the question of being, namely, the subject-verb-object language view and the rheomodic language view. In the first view, being is conceived through the analysis of language structure, where it is represented by subjects (particulars), objects, and relations (often universals). In the second view, there are different variations; however, the common idea is that the world's structure is revealed in the root verb of terms. This suggests a holistic and dynamic conception of being, where everything is in a continuous process of action. The book builds on analytic philosophy and explores metaphysical concepts such as space-time, modality, causation, indeterminism versus determinism, and mind and body. The book shows that in both Western and African thought, (i) similarities in different studies confirm that philosophy is a universal activity, (ii) differences within a context and beyond confirm the perspectival nature of human knowledge as individuals attempt to interpret reality, and (iii) language influences the conceptualization of being in a particular area. One of the novel aspects is the development of visual and mathematical African models of space and time.
Download or read book Geometric Formulas written by Speedy Publishing and published by Speedy Publishing LLC. This book was released on 2014-09-04 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is no doubt about the fact that our daily lives consistently revolve around mathematics. Whether one knows it or not, just about everything that is seen and felt throughout the day involves some kind of math. The study of geometry can give students a better understanding of how buildings, furniture, vehicles, and other infrastructural models are designed and built. Everything that is created and built around us has involved some kind of geometry. A geometric formulas study guide can help students to not only understand the formulas, but also to retain them within their memories to make solving problems and understanding a much easier task.
Download or read book Geometry written by John Tabak and published by Infobase Publishing. This book was released on 2014-05-14 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Greek ideas about geometry, straight-edge and compass constructions, and the nature of mathematical proof dominated mathematical thought for about 2,000 years.
Download or read book A History of Non Euclidean Geometry written by Boris A. Rosenfeld and published by Springer Science & Business Media. This book was released on 2012-09-08 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.
Download or read book The Math Book written by DK and published by Penguin. This book was released on 2019-09-03 with total page 711 pages. Available in PDF, EPUB and Kindle. Book excerpt: See how math's infinite mysteries and beauty unfold in this captivating educational book! Discover more than 85 of the most important mathematical ideas, theorems, and proofs ever devised with this beautifully illustrated book. Get to know the great minds whose revolutionary discoveries changed our world today. You don't have to be a math genius to follow along with this book! This brilliant book is packed with short, easy-to-grasp explanations, step-by-step diagrams, and witty illustrations that play with our ideas about numbers. What is an imaginary number? Can two parallel lines ever meet? How can math help us predict the future? All will be revealed and explained in this encyclopedia of mathematics. It's as easy as 1-2-3! The Math Book tells the exciting story of how mathematical thought advanced through history. This diverse and inclusive account will have something for everybody, including the math behind world economies and espionage. This book charts the development of math around the world, from ancient mathematical ideas and inventions like prehistoric tally bones through developments in medieval and Renaissance Europe. Fast forward to today and gain insight into the recent rise of game and group theory. Delve in deeper into the history of math: - Ancient and Classical Periods 6000 BCE - 500 CE - The Middle Ages 500 - 1500 - The Renaissance 1500 - 1680 - The Enlightenment 1680 - 1800 - The 19th Century 1800 - 1900 - Modern Mathematics 1900 - Present The Series Simply Explained With over 7 million copies sold worldwide to date, The Math Book is part of the award-winning Big Ideas Simply Explained series from DK Books. It uses innovative graphics along with engaging writing to make complex subjects easier to understand.
Download or read book Mathematics for Earth Science and Geography written by Cyril Fleurant and published by Springer. This book was released on 2018-09-19 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook presents a unique comprehensive overview on Mathematics in Earth Sciences and Geography. It deals with fundamental theoretical and applied mathematics, needed by bachelor students in a wide range of subjects. The book is illustrated with many examples and over a hundred practical exercises, with solutions included in the book. In addition, this textbook highlights numerical resources by using two free software packages (R and Xcas) and introducing their use.
Download or read book Mathematizing Space written by Vincenzo De Risi and published by Birkhäuser. This book was released on 2015-01-31 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the papers of the conference held in Berlin, Germany, 27-29 August 2012, on 'Space, Geometry and the Imagination from Antiquity to the Modern Age'. The conference was a joint effort by the Max Planck Institute for the History of Science (Berlin) and the Centro die Ricerca Matematica Ennio De Giorgi (Pisa).
Download or read book Analytic Geometry of Space written by Virgil Snyder and published by Forgotten Books. This book was released on 2015-06-24 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Analytic Geometry of Space In this book, which is planned for an introductory course, the first eight chapters include the subjects usually treated in rectangular coordinates. They presuppose as much knowledge of algebra, geometry, and trigonometry as is contained in the major requirement of the College Entrance Examination Board, and as much plane analytic geometry as is contained in the better elementary textbooks. In this portion, proofs of theorems from more advanced subjects in algebra are supplied as needed. Among the features of this part are the development of linear systems of planes, plane coordinates, the concept of infinity, the treatment of imaginaries, and the distinction between centers and vertices of quadric surfaces. The study of this portion can be regarded as a first course, not demanding more than thirty or forty lessons. In Chapter IX tetrahedral coordinates are introduced by means of linear transformations, under which various invariant properties are established. These coordinates are used throughout the next three chapters. The notation is so chosen that no ambiguity can arise between tetrahedral and rectangular systems. The selection of subject matter is such as to be of greatest service for further study of algebraic geometry. In Chapter XIII a more advanced knowledge of plane analytic geometry is presupposed, but the part involving Plücker's numbers may be omitted without disturbing the continuity of the subject. In the last chapter extensive use is made of the calculus, including the use of partial differentiation and of the element of arc. The second part will require about fifty lessons. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book Divine Proportions written by Norman John Wildberger and published by . This book was released on 2005 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: "... introduces a remarkable new approach to trigonometry and Euclidean geometry, with dramatic implications for mathematics teaching, industrial applications and the direction of mathematical research in geometry" -- p. vii.
Download or read book Trigonometry written by I.M. Gelfand and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a sense, trigonometry sits at the center of high school mathematics. It originates in the study of geometry when we investigate the ratios of sides in similar right triangles, or when we look at the relationship between a chord of a circle and its arc. It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. It also has many applications to physics, astronomy, and other branches of science. It is a very old subject. Many of the geometric results that we now state in trigonometric terms were given a purely geometric exposition by Euclid. Ptolemy, an early astronomer, began to go beyond Euclid, using the geometry of the time to construct what we now call tables of values of trigonometric functions. Trigonometry is an important introduction to calculus, where one stud ies what mathematicians call analytic properties of functions. One of the goals of this book is to prepare you for a course in calculus by directing your attention away from particular values of a function to a study of the function as an object in itself. This way of thinking is useful not just in calculus, but in many mathematical situations. So trigonometry is a part of pre-calculus, and is related to other pre-calculus topics, such as exponential and logarithmic functions, and complex numbers.
Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 2012 with total page 1480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
