Polygons
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Generalized Polygons
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Author : Hendrik,van Maldeghem
language : en
Publisher: Birkhäuser
Release Date : 2013-11-09
Generalized Polygons written by Hendrik,van Maldeghem and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with Mathematics categories.
This book is intended to be an introduction to the fascinating theory ofgeneralized polygons for both the graduate student and the specialized researcher in the field. It gathers together a lot of basic properties (some of which are usually referred to in research papers as belonging to folklore) and very recent and sometimes deep results. I have chosen a fairly strict geometrical approach, which requires some knowledge of basic projective geometry. Yet, it enables one to prove some typically group-theoretical results such as the determination of the automorphism groups of certain Moufang polygons. As such, some basic group-theoretical knowledge is required of the reader. The notion of a generalized polygon is a relatively recent one. But it is one of the most important concepts in incidence geometry. Generalized polygons are the building bricks of Tits buildings. They are the prototypes and precursors of more general geometries such as partial geometries, partial quadrangles, semi-partial ge ometries, near polygons, Moore geometries, etc. The main examples of generalized polygons are the natural geometries associated with groups of Lie type of relative rank 2. This is where group theory comes in and we come to the historical raison d'etre of generalized polygons. In 1959 Jacques Tits discovered the simple groups of type 3D by classifying the 4 trialities with at least one absolute point of a D -geometry. The method was 4 predominantly geometric, and so not surprisingly the corresponding geometries (the twisted triality hexagons) came into play. Generalized hexagons were born.
A Panoply Of Polygons
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Author : Claudi Alsina
language : en
Publisher: American Mathematical Society
Release Date : 2023-01-30
A Panoply Of Polygons written by Claudi Alsina and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-30 with Mathematics categories.
A Panoply of Polygons presents and organizes hundreds of beautiful, surprising and intriguing results about polygons with more than four sides. (A Cornucopia of Quadrilaterals, a previous volume by the same authors, thoroughly explored the properties of four-sided polygons.) This panoply consists of eight chapters, one dedicated to polygonal basics, the next ones dedicated to pentagons, hexagons, heptagons, octagons and many-sided polygons. Then miscellaneous classes of polygons are explored (e.g., lattice, rectilinear, zonogons, cyclic, tangential) and the final chapter presents polygonal numbers (figurate numbers based on polygons). Applications, real-life examples, and uses in art and architecture complement the presentation where many proofs with a visual nature are included. A Panoply of Polygons can be used as a supplement to a high school or college geometry course. It can also be used as a source for group projects or extra-credit assignments. It will appeal, and be accessible to, anyone with an interest in plane geometry. Claudi Alsina and Roger Nelsen are, jointly and individually, the authors of thirteen previous MAA/AMS books. Those books, and this one, celebrate and illuminate the power of visualization in learning, teaching, and creating mathematics.
If You Were A Polygon
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Author : Marcie Aboff
language : en
Publisher: Capstone
Release Date : 2010
If You Were A Polygon written by Marcie Aboff and has been published by Capstone this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Juvenile Nonfiction categories.
The creative examples, simple text, and art in this series help students learn primary math concepts.
Polygons
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Author : David L. Stienecker
language : en
Publisher: Cavendish Square Publishing
Release Date : 1997
Polygons written by David L. Stienecker and has been published by Cavendish Square Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Juvenile Nonfiction categories.
Identifies various kinds of polygons and uses activities, puzzles, and games to explore these shapes.
Polygons Polyominoes And Polycubes
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Author : A. J. Guttmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-18
Polygons Polyominoes And Polycubes written by A. J. Guttmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-18 with Science categories.
The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?rst sight, it seems surprising that it hasn’t been solved. It is however perhaps the simplest member of a large class of such problems that have resisted all attempts at their exact solution. These are all problems that are easy to state and look as if they should be solvable. They include percolation, in its various forms, the Ising model of ferromagnetism, polyomino enumeration, Potts models and many others. These models are of intrinsic interest to mathematicians and mathematical physicists, but can also be applied to many other areas, including economics, the social sciences, the biological sciences and even to traf?c models. It is the widespread applicab- ity of these models to interesting phenomena that makes them so deserving of our attention. Here however we restrict our attention to the mathematical aspects. Here we are concerned with collecting together most of what is known about polygons, and the closely related problems of polyominoes. We describe what is known, taking care to distinguish between what has been proved, and what is c- tainlytrue,but has notbeenproved. Theearlierchaptersfocusonwhatis knownand on why the problems have not been solved, culminating in a proof of unsolvability, in a certain sense. The next chapters describe a range of numerical and theoretical methods and tools for extracting as much information about the problem as possible, in some cases permittingexactconjecturesto be made.
Polygons In Our World
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Author : Brian Armstrong
language : en
Publisher: The Rosen Publishing Group, Inc
Release Date : 2014-12-15
Polygons In Our World written by Brian Armstrong and has been published by The Rosen Publishing Group, Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-15 with Juvenile Nonfiction categories.
Shapes are everywhere, and understanding geometric properties is an essential part of math education. A comprehensive introduction to geometry is told through relatable narratives and real-world situations, teaching readers how to recognize geometry in everyday life. Engaging visuals and age-appropriate content work together to reinforce complex math concepts. Polygons are all around us, and readers will learn how to recognize them and their attributes after reading this exciting narrative. This volume meets CCSS Math Standard 2.G.A.1.
What Are Polygons
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Author : Dorian Long
language : en
Publisher: The Rosen Publishing Group, Inc
Release Date : 2014-08-01
What Are Polygons written by Dorian Long and has been published by The Rosen Publishing Group, Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-01 with Juvenile Nonfiction categories.
Shapes are everywhere, and understanding geometric properties is an essential part of math education. A comprehensive introduction to geometry is told through relatable narratives and real-world situations, teaching readers how to recognize geometry in everyday life. Engaging visuals and age-appropriate content work together to reinforce complex math concepts. Math students will learn how to recognize and draw their own polygons through this exciting narrative. This volume meets CCSS Math Standard 2.G.A.1.
Polygons Galore
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Author : Dana T. Johnson
language : en
Publisher: Routledge
Release Date : 2021-09-03
Polygons Galore written by Dana T. Johnson and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-03 with Education categories.
Polygons Galore! is a mathematics unit for high-ability learners in grades 3-5 focusing on 2-D and 3-D components of geometry by exploring polygons and polyhedra and their properties. The van Hiele levels of geometric understanding provide conceptual underpinnings for unit activities. The unit consists of nine lessons that include student discovery of properties of polygons and polyhedra, investigations for finding areas of triangles and quadrilaterals, study of the Platonic solids, and real-world applications of polygons and polyhedra. It also includes activities related to identifying, comparing, and analyzing polygons by using properties of the polygons; constructing meanings for geometric terms; developing strategies to find areas of specific polygons; identifying and building regular and nonregular polyhedra; and recognizing geometric ideas and relationships as applied in daily life and in other disciplines, such as art. Grades 3-5
Picturing Polygons
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Author : Catherine Anderson
language : en
Publisher:
Release Date : 1996
Picturing Polygons written by Catherine Anderson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Emphasis on mathematical thinking and teaching strategies on using shapes to create polygons. Students can also investigate various properties of triangles, quadrilaterals, and regular polygons.
Polygon And Its Parts Basic Geometrical Ideas
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Author :
language : en
Publisher: EKalam
Release Date :
Polygon And Its Parts Basic Geometrical Ideas written by and has been published by EKalam this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Objectives :- Adjacent and Opposite sides, Diagonal, Different types of polygons based on their side, Triangle, Quadrilateral, Pentagon, Hexagon, Heptagon and Octagon.