Number Shape Symmetry

Author : Diane L. Herrmann,Paul J. Sally, Jr.
Publisher : CRC Press
Page : 446 pages
File Size : 44,7 Mb
Release : 2012-10-18
Category : Mathematics
ISBN : 9781466554641

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Number, Shape, & Symmetry by Diane L. Herrmann,Paul J. Sally, Jr. Pdf

Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.

Author : Diane L. Herrmann,Paul J. Sally Jr.
Publisher : CRC Press
Page : 444 pages
File Size : 55,7 Mb
Release : 2012-10-18
Category : Mathematics
ISBN : 9781466554658

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Number, Shape, & Symmetry by Diane L. Herrmann,Paul J. Sally Jr. Pdf

Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors' successful work with undergraduate students at the University of Chicago, seventh

Author : Kristopher Tapp
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 46,6 Mb
Release : 2011-12-02
Category : Mathematics
ISBN : 1461402999

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Symmetry by Kristopher Tapp Pdf

This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler’s formula, irrational numbers, countable sets, permutations, and a proof of the Pythagorean Theorem. All of these topics serve a single compelling goal: understanding the mathematical patterns underlying the symmetry that we observe in the physical world around us. The exposition is engaging, precise and rigorous. The theorems are visually motivated with intuitive proofs appropriate for the intended audience. Students from all majors will enjoy the many beautiful topics herein, and will come to better appreciate the powerful cumulative nature of mathematics as these topics are woven together into a single fascinating story about the ways in which objects can be symmetric.

Author : L.Christine Kinsey,Teresa E. Moore
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 42,7 Mb
Release : 2006-05-09
Category : Mathematics
ISBN : 1930190093

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Symmetry, Shape and Space by L.Christine Kinsey,Teresa E. Moore Pdf

This book will appeal to at least three groups of readers: prospective high school teachers, liberal arts students, and parents whose children are studying high school or college math. It is modern in its selection of topics, and in the learning models used by the authors. The book covers some exciting but non-traditional topics from the subject area of geometry. It is also intended for undergraduates and tries to engage their interest in mathematics. Many innovative pedagogical modes are used throughout.

Author : Alan Holden
Publisher : Courier Corporation
Page : 218 pages
File Size : 52,7 Mb
Release : 1991-01-01
Category : Mathematics
ISBN : 0486268519

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Shapes, Space, and Symmetry by Alan Holden Pdf

Explains structure of nine regular solids and many semiregular solids and demonstrates how they can be used to explain mathematics. Instructions for cardboard models. Over 300 illustrations. 1971 edition.

Author : Ilya Sinitsky
Publisher : Springer
Page : 378 pages
File Size : 42,8 Mb
Release : 2016-11-25
Category : Education
ISBN : 9789463006996

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Change and Invariance by Ilya Sinitsky Pdf

"What is the connection between finding the amount of acid needed to reach the desired concentration of a chemical solution, checking divisibility by a two-digit prime number, and maintaining the perimeter of a polygon while reducing its area? The simple answer is the title of this book.The world is an interplay of variation and constancy – a medley of differences and similarities – and this change and invariance is, largely, a language of science and mathematics. This book proposes a unique approach for developing mathematical insight through the perspective of change and invariance as it applies to the properties of numbers and shapes.After a short introductory chapter, each of the following chapters presents a series of evolving activities for students that focus on a specific aspect of interplay between change and invariance. Each activity is accompanied by detailed mathematical explanations and a didactic discussion. The assignments start with tasks familiar from the school curriculum, but progress beyond the menial to lead to sophisticated generalizations. Further activities are suggested to augment the chapter’s theme. Some examples: “How to represent all the integers from zero to 1000 using ten fingers?”, “How to win at the game of Nim?”, “Why do different square lattice polygons with the same area often have the same perimeter?” This book can be used as a textbook for pre-service mathematics teachers and is primarily intended for their academic instructors. Essentially, students, teachers and anyone interested in elementary mathematics will enjoy the elegant solutions provided for the plethora of problems in elementary mathematics through the systematic approach of invariance and change."

Author : David Clemson,Wendy Clemson
Publisher : Nelson Thornes
Page : 164 pages
File Size : 42,7 Mb
Release : 2002
Category : Geometrical constructions
ISBN : 9780748763191

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Measures, Shape and Space by David Clemson,Wendy Clemson Pdf

Maths Action Plans is a series of four books for Years 4-6/P5-7, offering flexible, supportive teacher and pupil resources and coherent coverage of the five strands of the Framework for Teaching Mathematics. The series provides inspiring, flexible activities that can be fitted into any maths scheme. Each title contains: clear learning objectives, linked to the Framework for Teaching Maths, the National Curriculum Programme of Study and the 5-14 National Guidelines for Mathematics; lesson plans with up to three levels of differentiation; supplementary activities for consolidation or linked work; and suggestions for the application of ICT skills.

Author : Joan Akers
Publisher : Unknown
Page : 0 pages
File Size : 40,7 Mb
Release : 2004
Category : Arithmetic
ISBN : 0201378175

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Shapes, Halves, and Symmetry by Joan Akers Pdf

Author : Thomas Canavan
Publisher : The Rosen Publishing Group, Inc
Page : 50 pages
File Size : 51,6 Mb
Release : 2011-12-15
Category : Juvenile Nonfiction
ISBN : 9781448866960

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Shapes and Symmetry by Thomas Canavan Pdf

Provides mathematical exercises to strengthen the skills of finding balance and order in shapes.

Author : Anonim
Publisher : Unknown
Page : 252 pages
File Size : 49,5 Mb
Release : 2006
Category : Fractions
ISBN : 0328167398

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Shapes, Halves, and Symmetry by Anonim Pdf

Author : Ian Stewart
Publisher : OUP Oxford
Page : 152 pages
File Size : 42,6 Mb
Release : 2013-05-30
Category : Mathematics
ISBN : 9780191652745

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Symmetry: A Very Short Introduction by Ian Stewart Pdf

In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Author : Niall Galloway
Publisher : Jessica Kingsley Publishers
Page : 200 pages
File Size : 45,8 Mb
Release : 2018-09-01
Category : Health & Fitness
ISBN : 9781912085125

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Seeking Symmetry by Niall Galloway Pdf

Seeking Symmetry: Finding patterns in human health offers a guide through the overwhelming mass of data generated by contemporary science. Starved for the knowledge that would best help us stay healthy, we are simultaneously glutted with an overload of information about the human body. Amidst ubiquitous talk that patient-centred care and lifestyle changes are the keys to personal health, self-neglect and medical overtreatment nevertheless prevail. The body is rich with symmetries, many of them unknown to us who live in these bodies. Symmetry-seeking reveals certain patterns for understanding the information we have about the body, patterns whose roots lie in embryonic development and in evolution. The book's exploration will guide readers through the parts of their own bodies and introduce tangible, visible examples of symmetry, not only right and left but up and down, male and female, inside and out, as well as symmetries between humans and other species.It presents the symmetries of the body's internal structures that, despite their complexity, are nevertheless simple to understand when viewed with an eye for pattern.Through both words and images, this book will illustrate the most foundational of the principles, structures, and processes that decide how bodies function.A core purpose of the book is to present this knowledge through a lens that makes the information meaningful, by modelling the habit of symmetry-seeking.

Author : Alex Berke
Publisher : MIT Press
Page : 165 pages
File Size : 52,9 Mb
Release : 2020-02-18
Category : Mathematics
ISBN : 9780262538923

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Beautiful Symmetry by Alex Berke Pdf

A coloring book that invites readers to explore symmetry and the beauty of math visually. Beautiful Symmetry is a coloring book about math, inviting us to engage with mathematical concepts visually through coloring challenges and visual puzzles. We can explore symmetry and the beauty of mathematics playfully, coloring through ideas usually reserved for advanced courses. The book is for children and adults, for math nerds and math avoiders, for educators, students, and coloring enthusiasts. Through illustration, language that is visual, and words that are jargon-free, the book introduces group theory as the mathematical foundation for discussions of symmetry, covering symmetry groups that include the cyclic groups, frieze groups, and wallpaper groups. The illustrations are drawn by algorithms, following the symmetry rules for each given group. The coloring challenges can be completed and fully realized only on the page; solutions are provided. Online, in a complementary digital edition, the illustrations come to life with animated interactions that show the symmetries that generated them. Traditional math curricula focus on arithmetic and the manipulation of numbers, and may make some learners feel that math is not for them. By offering a more visual and tactile approach, this book shows how math can be for everyone. Combining the playful and the pedagogical, Beautiful Symmetry offers both relaxing entertainment for recreational colorers and a resource for math-curious readers, students, and educators.

Author : Michel Planat
Publisher : Unknown
Page : 206 pages
File Size : 45,7 Mb
Release : 2020
Category : Electronic
ISBN : 3039366874

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Number Theory and Symmetry by Michel Planat Pdf

According to Carl Friedrich Gauss (1777-1855), mathematics is the queen of the sciences--and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory. In particular, it highlights connections between symmetry and number theory, quantum computing and elementary particles (thanks to 3-manifolds), and other branches of mathematics (such as probability spaces) and revisits standard subjects (such as the Sieve procedure, primality tests, and Pascal's triangle). The book should be of interest to all mathematicians, and physicists.

Author : Joan Akers
Publisher : Unknown
Page : 252 pages
File Size : 41,8 Mb
Release : 1998
Category : Juvenile Nonfiction
ISBN : 1572326565

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Shapes, Halves, and Symmetry by Joan Akers Pdf