Some Adventures In Euclidean Geometry

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Some Adventures In Euclidean Geometry

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Author : Michael de Villiers
language : en
Publisher: Dynamic Mathematics Learning
Release Date : 2009-09-08

Some Adventures In Euclidean Geometry written by Michael de Villiers and has been published by Dynamic Mathematics Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-08 with Education categories.

This book seeks to actively involve the reader in the heuristic processes of conjecturing, discovering, formulating, classifying, defining, refuting, proving, etc. within the context of Euclidean geometry. The book deals with many interesting and beautiful geometric results, which have only been discovered during the past 300 years such as the Euler line, the theorems of Ceva, Napoleon, Morley, Miquel, Varignon, etc. Extensive attention is also given to the classification of the quadrilaterals from the symmetry of a side-angle duality. Many examples lend themselves excellently for exploration on computer with dynamic geometry programs such as Sketchpad. The book is addressed primarily to university or college lecturers involved in the under-graduate or in-service training of high school mathematics teachers, but may also interest teachers who are looking for enrichment material, and gifted high school mathematics pupils.

Adventures In Mathematics

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Author : Martin A. Moskowitz
language : en
Publisher: World Scientific
Release Date : 2003

Adventures In Mathematics written by Martin A. Moskowitz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

Though elementary in nature, this book deals with fundamental issues in mathematics OCo number, algebra, geometry (both Euclidean and non-Euclidean) and topology. These subjects, on an advanced level, are the same ones with which much of current mathematical research is concerned and were themselves research topics of earlier periods. The material is very suitable both for advanced high school students and for college students interested in elementary mathematics from a higher standpoint. It will also be very useful to high school teachers seeking an overview of their subject matter. Contents: What is a Number?: The Positive Integers; The Integers; The Rational Numbers; The Real Numbers; The Integers Revisited; The Complex Numbers; Polynomials and Other Analogues of the Integers; The Algebra on a Dial; Groups, Finite Fields and Linear Algebra: Introduction to Groups and Their Actions; Applications to Finite Fields and the Theory of Numbers; Linear Algebra; Two- and Three-Dimensional Geometry and Topology: The Euclidean Case; Elliptic and Hyperbolic Geometry; Some Two- and Three-Dimensional Topology. Readership: High school and college teachers and students; college pre-calculus teachers and students; general readers with an interest in mathematics but a limited background."

Adventures In Dynamic Geometry

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Author : Gerry Stahl
language : en
Publisher: Lulu.com
Release Date : 2015-10-06

Adventures In Dynamic Geometry written by Gerry Stahl and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-06 with Education categories.

Math games and workbooks with topics for online small groups of teachers or students to collaboratively learn dynamic geometry. The approach is based on "Translating Euclid." The many GeoGebra files used in VMT courses are pictured in the workbook. Several versions of the workbooks are available, including the version used in WinterFest 2013 and analyzed in "Translating Euclid" and "Constructing Dynamic Triangles Together." Also includes the content of a game version that is available as a GeoGebraBook.

Crocheting Adventures With Hyperbolic Planes

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Author : Daina Taimina
language : en
Publisher: CRC Press
Release Date : 2018-02-19

Crocheting Adventures With Hyperbolic Planes written by Daina Taimina and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-19 with Mathematics categories.

Winner, Euler Book Prize, awarded by the Mathematical Association of America. With over 200 full color photographs, this non-traditional, tactile introduction to non-Euclidean geometries also covers early development of geometry and connections between geometry, art, nature, and sciences. For the crafter or would-be crafter, there are detailed instructions for how to crochet various geometric models and how to use them in explorations. New to the 2nd Edition; Daina Taimina discusses her own adventures with the hyperbolic planes as well as the experiences of some of her readers. Includes recent applications of hyperbolic geometry such as medicine, architecture, fashion & quantum computing.

Learning To Teach In Post Apartheid South Africa

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Author : Yusuf Sayed
language : en
Publisher: AFRICAN SUN MeDIA
Release Date : 2018-11-28

Learning To Teach In Post Apartheid South Africa written by Yusuf Sayed and has been published by AFRICAN SUN MeDIA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-28 with Self-Help categories.

Teacher education programmes seek to provide student teachers with the knowledge and expertise to provide qualtiy teaching and learning in a diverse and challenging school context. Learning to Teach in post-apartheid South Africa: Student Teachers' Encounters with Initial Teacher Education addresses the complexities of teacher education programmes in preparing students to teach. It adds to the knowledge about teacher education, contributing critical understanding of education and the schooling system. The book provides important insights to deepen researchers, academics, teacher education providers, policy-makers, and students' understanding of the importance to address equity, redress, and quality in South African educaiton in a post-apartheid era. This book further helps to build student teachers' capacities to work creatively and to become active and critical agents of transformation. It ultimately outlines the challenges face in designing and delivering successful Inital Teacher Education programmes, and the impact this has on delivering equitable and qualtiy education.

Non Euclidean Adventures On The Lenart Sphere

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Author : Istvan Lenart
language : en
Publisher:
Release Date : 1995-11-01

Non Euclidean Adventures On The Lenart Sphere written by Istvan Lenart and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-01 with Mathematics categories.

Use Of Hydrocolloids To Control Food Appearance Flavor Texture And Nutrition

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Author : Amos Nussinovitch
language : en
Publisher: John Wiley & Sons
Release Date : 2023-01-04

Use Of Hydrocolloids To Control Food Appearance Flavor Texture And Nutrition written by Amos Nussinovitch and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-04 with Technology & Engineering categories.

Use of Hydrocolloids to Control Food Appearance, Flavor, Texture, and Nutrition A thoroughly up-to-date and forward-looking presentation of the use of hydrocolloids in food In Use of Hydrocolloids to Control Food Appearance, Flavor, Texture, and Nutrition, a team of distinguished food researchers combines comprehensive and authoritative discussions on the conventional use of hydrocolloids to influence shape, structure and organoleptic properties of foods with exciting and emerging areas of innovation, such as texturing for 3D printing and enhancement of food nutrition. The book explores the four principal quality factors of food: appearance, flavor, texture and nutrition, and introduces students and food technologists to the myriad uses of hydrocolloids. It also presents illustrations of relevant commercial food products that rely on hydrocolloids for their appeal, as well as recipes exemplifying the unique abilities of particular hydrocolloids. Readers will also find: A thorough introduction to the use of hydrocolloids to control food size and shape, including the manipulation of select geometrical properties of foods A comprehensive exploration of the use of hydrocolloids to modulate food color and gloss, including the psychological impact of those properties Practical discussions pertaining to the modification of food taste and odor using hydrocolloids A thorough description of the ways in which hydrocolloids are used to improve crispy, crunchy and crackly foods Perfect for food scientists working in product development and food engineers, Use of Hydrocolloids to Control Food Appearance, Flavor, Texture, and Nutrition is sure to earn a place in the libraries of research chefs, as well as food chemists, food microbiologists and food technologists.

Euclidean Non Euclidean And Transformational Geometry

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Author : Shlomo Libeskind
language : en
Publisher: Springer Nature
Release Date : 2024-10-22

Euclidean Non Euclidean And Transformational Geometry written by Shlomo Libeskind and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-22 with Mathematics categories.

This undergraduate textbook provides a comprehensive treatment of Euclidean and transformational geometries, supplemented by substantial discussions of topics from various non-Euclidean and less commonly taught geometries, making it ideal for both mathematics majors and pre-service teachers. Emphasis is placed on developing students' deductive reasoning skills as they are guided through proofs, constructions, and solutions to problems. The text frequently emphasizes strategies and heuristics of problem solving including constructing proofs (Where to begin? How to proceed? Which approach is more promising? Are there multiple solutions/proofs? etc.). This approach aims not only to enable students to successfully solve unfamiliar problems on their own, but also to impart a lasting appreciation for mathematics. The text first explores, at a higher level and in much greater depth, topics that are normally taught in high school geometry courses: definitions and axioms, congruence, circles and related concepts, area and the Pythagorean theorem, similarity, isometries and size transformations, and composition of transformations. Constructions and the use of transformations to carry out constructions are emphasized. The text then introduces more advanced topics dealing with non-Euclidean and less commonly taught topics such as inversive, hyperbolic, elliptic, taxicab, fractal, and solid geometries. By examining what happens when one or more of the building blocks of Euclidean geometry are altered, students will gain a deeper understanding of and appreciation for Euclidean concepts. To accommodate students with different levels of experience in the subject, the basic definitions and axioms that form the foundation of Euclidean geometry are covered in Chapter 1. Problem sets are provided after every section in each chapter and include nonroutine problems that students will enjoy exploring. While not necessarily required, the appropriate use of freely available dynamic geometry software and other specialized software referenced in the text is strongly encouraged; this is especially important for visual learners and for forming conjectures and testing hypotheses.

Joyce And Geometry

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Author : Ciaran McMorran
language : en
Publisher: University Press of Florida
Release Date : 2020-01-15

Joyce And Geometry written by Ciaran McMorran and has been published by University Press of Florida this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-15 with Literary Criticism categories.

In a paradigm shift away from classical understandings of geometry, nineteenth-century mathematicians developed new systems that featured surprising concepts such as the idea that parallel lines can curve and intersect. Providing evidence to confirm much that has largely been speculation, Joyce and Geometry reveals the full extent to which the modernist writer James Joyce was influenced by the radical theories of non-Euclidean geometry. Through close readings of Ulysses, Finnegans Wake, and Joyce’s notebooks, Ciaran McMorran demonstrates that Joyce’s experiments with nonlinearity stem from a fascination with these new mathematical concepts. He highlights the maze-like patterns traced by Joyce’s characters as they wander Dublin’s streets; he explores recurring motifs such as the topography of the Earth’s curved surface and time as the fourth dimension of space; and he investigates in detail the enormous influence of Giordano Bruno, Henri Poincaré, and other writers who were critical of the Euclidean tradition. Arguing that Joyce’s obsession with measuring and mapping space throughout his works encapsulates a modern crisis between geometric and linguistic modes of representation, McMorran delves into a major theme in Joyce’s work that has not been fully explored until now. A volume in the Florida James Joyce Series, edited by Sebastian D. G. Knowles

Shadows Of The Circle

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Author : Vagn Lundsgaard Hansen
language : en
Publisher: World Scientific
Release Date : 1998

Shadows Of The Circle written by Vagn Lundsgaard Hansen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

The aim of this book is to throw light on various facets of geometry through development of four geometrical themes. The first theme is about the ellipse, the shape of the shadow east by a circle. The next, a natural continuation of the first, is a study of all three types of conic sections, the ellipse, the parabola and the hyperbola. The third theme is about certain properties of geometrical figures related to the problem of finding the largest area that can be enclosed by a curve of given length. This problem is called the isoperimetric problem. In itself, this topic contains motivation for major parts of the curriculum in mathematics at college level and sets the stage for more advanced mathematical subjects such as functions of several variables and the calculus of variations. Here, three types of conic section are discussed briefly. The emergence of non-Euclidean geometries in the beginning of the nineteenth century represents one of the dramatic episodes in the history of mathematics. In the last theme the non-Euclidean geometry in the Poincare disc model of the hyperbolic plane is developed.