Elements of Geometry
This classic geometry textbook offers a clear and concise introduction to the principles and concepts of the subject, with a particular focus on practical applications. From triangles and polygons to circles and conic sections, the book covers a wide range of topics, providing students with a solid foundation for further study and exploration.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Cloudy With a Chance of Marriage
This textbook provides a comprehensive introduction to the principles of geometry and trigonometry, with a focus on adapting these concepts for use in the United States. With clear explanations and helpful examples, this book is an essential resource for students of mathematics at all levels.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Theory and Practice of Gauging, Demonstrated in a Short and Easy Method
First published in 1835, this practical guide to gauging - the measurement of the volume of liquids - offers a concise and accessible introduction to the subject. Shirtcliffe's straightforward approach makes it an ideal reference for anyone involved in the shipping, brewing, or distilling industries.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Problems in Astronomy, Surveying, and Navigation
As a renowned mathematician and astronomer, the author of this book provides a rigorous yet accessible approach to solving complex problems in astronomical mechanics, surveying, and navigation. From basic trigonometry to advanced calculus, readers will gain a deep understanding of the mathematical principles behind these fields.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Plane and Solid Geometry
First published in 1908, this textbook provides a thorough introduction to the principles of plane and solid geometry, with an emphasis on practical applications in engineering and architecture. The book covers topics such as Euclidean geometry, congruence, similarity, and coordinate geometry, and includes numerous exercises and examples to facilitate learning. The authors were both prominent mathematicians and educators of their time, and their clear and concise prose makes this a valuable resource for students and teachers alike.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Young Gentleman’s Arithmetick, and Geometry
This classic textbook provides a comprehensive introduction to the principles of arithmetic and geometry. Aimed at the young gentleman of the Georgian era, the book covers all the essential topics in these two fields, including arithmetic operations, fractions, decimals, and basic geometry. The author's clear and concise style makes this an easy-to-follow resource for students of all levels.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Creative Approaches in Dementia Care
This comprehensive guide to plane geometry is an essential resource for any student or teacher of mathematics. Covering a range of topics, including lines, angles, triangles, circles, and polygons, this text provides clear explanations and numerous examples to help readers master the subject. With its engaging and accessible writing style, this book is an ideal choice for anyone looking to improve their understanding of geometry.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Self-Examinations in Euclid
This classic textbook on Euclidean geometry offers clear explanations and numerous practice problems, making it an ideal resource for students and teachers. First published in the mid-19th century, Wright's work remains a valuable reference for anyone seeking a solid foundation in geometry.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Geometrical Analysis, and Geometry of Curve Lines
This book is an advanced textbook on geometry and mathematical analysis, written in the 19th century for students of natural philosophy. Leslie covers a wide range of topics, from the properties of curves and surfaces to the principles of calculus and differential equations.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Apocalyptic Realm
This classic textbook has been used by generations of students to learn the principles of geometry. Based on the work of the famous Scottish mathematician John Playfair, it provides a clear and concise introduction to the subject. With its highly accessible style and comprehensive coverage, Elements of Geometry is an essential resource for anyone studying mathematics.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elements of Geometry and Trigonometry Translated From the French of A.M. Legendre by David Brewster
This textbook offers a comprehensive introduction to geometry and trigonometry, including key formulas and problem-solving techniques. The translation by David Brewster improves upon the French original, making it more accessible to American students. A must-have for anyone studying mathematics.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Euclid’s Elements of Geometry, the First Six Books
The Elements of Geometry is a classic mathematical work that provides readers with a foundation for the study of geometry. Written by the ancient Greek mathematician Euclid, the book outlines the basic principles of geometry and their applications in various areas of mathematics. This particular version is also supplemented with other topics like trigonometry, natural philosophy and astronomy, making it an essential tool for anyone who wants to learn about these subjects. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elements of Geometry, Containing the First Six Books of Euclid
A classic textbook on geometry, containing the foundational principles and theorems of the subject. Ideal for students and teachers of mathematics.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Elements of Geometry
This book is a comprehensive guide to the principles of geometry, drawing on the work of Euclid, Archimedes, and other ancient mathematicians. The author presents a clear and concise overview of the subject, with detailed explanations and examples that are easy to follow. This book is an essential resource for students of mathematics and scientific philosophy.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Description, Nature and General Use, of the Sector and Plain-Scale
This fascinating book provides a detailed introduction to the sector and plain-scale, important tools for navigation and surveying. It covers the basic principles and techniques of using these tools, with clear and concise explanations and practical examples. The book also includes a brief history of these instruments, and explores their uses in a range of fields, from astronomy to engineering. Whether you're a history buff, a mathematician, or just curious about the world around you, this book is a must-read.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Formulas of Plane and Spherical Trigonometry
In this book, Edwin Pliny Seaver provides students and computers with a comprehensive set of formulas for plane and spherical trigonometry. Whether you're looking to solve complex mathematical problems or simply brushing up on your trigonometry skills, this book is an invaluable resource. Seaver's clear explanations and detailed examples make even the most advanced formulas easy to understand.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Short History of Greek Mathematics
Explore the fascinating world of Greek mathematics with this concise and informative history. Covering the period from Thales to Euclid, this book provides an overview of the major concepts and figures in Greek mathematics, along with insights into how their work has influenced modern mathematics and science.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Famous Problems of Elementary Geometry (Year 1897)
This book, published in 1897, presents an overview of elementary geometry and its famous problems, such as the angle trisection and the duplication of the cube. The authors provide historical context and mathematical explanations, making it accessible to both students and enthusiasts of the subject. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Inductive Geometry, Or, an Analysis of the Relations of Form and Magnitude
This book is a comprehensive analysis of inductive geometry, starting with elementary ideas derived through our senses. The author presents a logical progression of reasoning to develop the present state of the science. It is an essential resource for anyone interested in the field of geometry and its history.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elements of Plane and Spherical Trigonometry
First published in the early 19th century, Gregory's classic textbook on trigonometry remains a valuable resource for students and practitioners of applied mathematics. Combining clear explanations with practical examples, the book covers a wide range of topics, from surveying and astronomy to geodesy and navigation.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Euclid’s Parallel Postulate
In this book, John William Withers thoroughly explores the parallel postulate of Euclidean geometry and its relationship to other geometrical systems. He presents compelling arguments for the postulate's validity and significance within the broader field of math. Mathematicians, students of geometry, and lovers of mathematical theory will find this book enriching.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Premi癡res Notions Du Calcul Des Quaternions
Learn the basics of quaternion calculus with this introductory book. Ideal for students, this book covers the fundamental concepts and mathematical operations used in quaternion calculus.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
R矇sum矇 De G矇om矇trie Analytique a Deux Et Trois Dimensions
This book provides a summary of analytical geometry in two and three dimensions, aimed at candidates for the French technical and engineering schools. It covers topics such as vectors, equations, and curves, offering valuable insights into the principles of geometry and their application in engineering. This book is a must-read for students of mathematics and engineering.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
My Biggest Easy to Color Book 4
This book is a revised edition of Euclid's Elements, a foundational work of geometry first published in 300 BCE. This edition corrects errors made in previous translations and includes restored demonstrations that were lost in ancient texts. A must-read for anyone interested in the history and development of mathematics and geometry.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Lessons in Industrial Drawing
This innovative textbook provides a comprehensive introduction to the world of industrial drawing, covering a wide range of techniques and approaches. With detailed instructions and step-by-step exercises, Mary Isabel Gilmore offers students a hands-on, practical approach to the art of drawing.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Analytical Geometry
This classic work on analytical geometry provides a comprehensive treatment of conic sections and their properties, as well as an appendix on descriptive geometry. With numerous examples and exercises, it is an ideal text for students and professionals alike.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Home for a Bunny
This book is an edition of Euclid's Elements, a foundational work in the field of mathematics. The edition includes additional notes and commentary by the editor, Edward Mann Langley, making it an excellent resource for students, scholars, and anyone interested in the history of mathematics.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Analytic Geometry
Siceloff's clear and concise approach to analytic geometry makes it accessible to learners of all levels, providing readers with the foundational knowledge they need to understand this critical field.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Advanced Geometry for High Schools
This classic textbook on geometry has been a staple in high school classrooms for more than a century. Covering both solid and analytical geometry, the book provides a rigorous and comprehensive introduction to the subject. With clear explanations and plenty of exercises, it is an essential resource for any student of geometry.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The First Six Books of the Elements of Euclid, With a Commentary and Geometrical Exercises
Euclid's Elements is one of the most influential works of non-fiction in history, and this edition includes a detailed commentary and additional exercises to enhance the reader's understanding. The included treatise on solid geometry and essay on ancient geometrical analysis are also valuable resources for students of mathematics and history alike. Lardner's writing is clear and concise, making this edition accessible to readers of all levels.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Lectures on Fractal Geometry
This book is based on a series of lectures at the Mathematics Department of the University of Jena, developed in the period from 1995 up to 2015. It is completed by additional material and extensions of some basic results from the literature to more general metric spaces.This book provides a clear introduction to classical fields of fractal geometry, which provide some background for modern topics of research and applications. Some basic knowledge on general measure theory and on topological notions in metric spaces is presumed.
A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic Sections
This mathematics text provides a thorough introduction to the principles of plane co-ordinate geometry, with specific applications to the straight line and conic sections. The authors provide numerous examples to help readers gain a deep understanding of the subject matter.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it.This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
In the Tradition of Thurston II
The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston's heritage. Thurston's ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, M繹bius structures, hyperbolic ends, cone 3-manifolds, Thurston's norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.
The American Heritage Desk Dictionary
The Fun Way to Master GeometryYour journey into the world of math continues with "Geometry Through Stories," the next exciting installment in Jenny Kellett's groundbreaking educational adventure series.This is no ordinary textbook; it's a thrilling ride through the captivating world of geometry, disguised as a page-turning mystery story. Our intrepid adventurers find themselves in a world where angles hide secret messages and shapes solve time-sensitive problems in mystical lands. From the basics of points, lines, and planes to complex geometrical transformations, each chapter brings a new challenge. The race is on. Through the adventures and challenges our characters face, students will master the key concepts of geometry, including: Basic geometric terms and definitionsProperties of 2D and 3D shapesAngle relationshipsTriangle properties and the Pythagorean theoremPerimeter, area, and volume calculationsTransformations and symmetryEach chapter ends with practice problems, giving students the chance to apply what they've learned in a practical, engaging way. These problems are designed to help reinforce the concepts, ensuring students have a strong grasp of geometry basics.Suitable for students in the 9th grade and up (age 14), this book is the perfect supplementary guide to classroom learning. Whether you're a parent looking to support your child's education, a teacher seeking creative resources, or a student eager for a unique, engaging approach to geometry, "Geometry Through Stories" is an indispensable tool on your mathematical journey.From author Jenny Kellett, the creator of "Algebra 1: The Mystery of the Algebraic Artifact," comes another blend of education and adventure. With "Geometry: Journey into the World of Shapes and Angles, " learning math has never been more thrilling! Order your copy today.
Seeing Four-Dimensional Space and Beyond
According to string theory, our universe exists in a 10- or 11-dimensional space. However, the idea the space beyond 3 dimensions seems hard to grasp for beginners. This book presents a way to understand four-dimensional space and beyond: with knots! Beginners can see high dimensional space although they have not seen it.With visual illustrations, we present the manipulation of figures in high dimensional space, examples of which are high dimensional knots and n-spheres embedded in the (n+2)-sphere, and generalize results on relations between local moves and knot invariants into high dimensional space.Local moves on knots, circles embedded in the 3-space, are very important to research in knot theory. It is well known that crossing changes are connected with the Alexander polynomial, the Jones polynomial, HOMFLYPT polynomial, Khovanov homology, Floer homology, Khovanov homotopy type, etc. We show several results on relations between local moves on high dimensional knots and their invariants.The following related topics are also introduced: projections of knots, knot products, slice knots and slice links, an open question: can the Jones polynomial be defined for links in all 3-manifolds? and Khovanov-Lipshitz-Sarkar stable homotopy type. Slice knots exist in the 3-space but are much related to the 4-dimensional space. The slice problem is connected with many exciting topics: Khovanov homology, Khovanv-Lipshits-Sarkar stable homotopy type, gauge theory, Floer homology, etc. Among them, the Khovanov-Lipshitz-Sarkar stable homotopy type is one of the exciting new areas; it is defined for links in the 3-sphere, but it is a high dimensional CW complex in general.Much of the book will be accessible to freshmen and sophomores with some basic knowledge of topology.
Geometry Through Stories
The Fun Way to Master GeometryYour journey into the world of math continues with "Geometry Through Stories," the next exciting installment in Jenny Kellett's groundbreaking educational adventure series.This is no ordinary textbook; it's a thrilling ride through the captivating world of geometry, disguised as a page-turning mystery story. Our intrepid adventurers find themselves in a world where angles hide secret messages and shapes solve time-sensitive problems in mystical lands. From the basics of points, lines, and planes to complex geometrical transformations, each chapter brings a new challenge. The race is on. Through the adventures and challenges our characters face, students will master the key concepts of geometry, including: Basic geometric terms and definitionsProperties of 2D and 3D shapesAngle relationshipsTriangle properties and the Pythagorean theoremPerimeter, area, and volume calculationsTransformations and symmetryEach chapter ends with practice problems, giving students the chance to apply what they've learned in a practical, engaging way. These problems are designed to help reinforce the concepts, ensuring students have a strong grasp of geometry basics.Suitable for students in the 9th grade and up (age 14), this book is the perfect supplementary guide to classroom learning. Whether you're a parent looking to support your child's education, a teacher seeking creative resources, or a student eager for a unique, engaging approach to geometry, "Geometry Through Stories" is an indispensable tool on your mathematical journey.From author Jenny Kellett, the creator of "Algebra 1: The Mystery of the Algebraic Artifact," comes another blend of education and adventure. With "Geometry: Journey into the World of Shapes and Angles, " learning math has never been more thrilling! Order your copy today.
Differential Heterogenesis
This book describes about unlike usual differential dynamics common in mathematical physics, heterogenesis is based on the assemblage of differential constraints that are different from point to point. The construction of differential assemblages will be introduced in the present study from the mathematical point of view, outlining the heterogeneity of the differential constraints and of the associated phase spaces, that are continuously changing in space and time. If homogeneous constraints well describe a form of swarm intelligence or crowd behaviour, it reduces dynamics to automatisms, by excluding any form of imaginative and creative aspect. With this study we aim to problematize the procedure of homogeneization that is dominant in life and social science and to outline the dynamical heterogeneity of life and its affective, semiotic, social, historical aspects. Particularly, the use of sub-Riemannian geometry instead of Riemannian one allows to introduce disjointed and autonomous areas in the virtual plane. Our purpose is to free up the dynamic becoming from any form of unitary and totalizing symmetry and to develop forms, action, thought by means of proliferation, juxtaposition, and disjunction devices. After stating the concept of differential heterogenesis with the language of contemporary mathematics, we will face the problem of the emergence of the semiotic function, recalling the limitation of classical approaches (Hjelmslev, Saussure, Husserl) and proposing a possible genesis of it from the heterogenetic flow previously defined. We consider the conditions under which this process can be polarized to constitute different planes of Content (C) and Expression (E), each one equipped with its own formed substances. A possible (but not unique) process of polarization is constructed by means of spectral analysis, that is introduced to individuate E/C planes and their evolution. The heterogenetic flow, solution of differential assemblages, gives rise to forms that are projected onto the planes, offering a first referring system for the flow, that constitutes a first degree of semiosis.
Local Systems in Algebraic-Arithmetic Geometry
The topological fundamental group of a smooth complex algebraic variety is poorly understood. One way to approach it is to consider its complex linear representations modulo conjugation, that is, its complex local systems. A fundamental problem is then to single out the complex points of such moduli spaces which correspond to geometric systems, and more generally to identify geometric subloci of the moduli space of local systems with special arithmetic properties. Deep conjectures have been made in relation to these problems. This book studies some consequences of these conjectures, notably density, integrality and crystallinity properties of some special loci.This monograph provides a unique compelling and concise overview of an active area of research and is useful to students looking to get into this area. It is of interest to a wide range of researchers and is a useful reference for newcomers and experts alike.
Polyhedra and Beyond
This volume collects papers based on talks given at the conference "Geometrias'19: Polyhedra and Beyond", held in the Faculty of Sciences of the University of Porto between September 5-7, 2019 in Portugal. These papers explore the conference's theme from an interdisciplinary standpoint, all the while emphasizing the relevance of polyhedral geometry in contemporary academic research and professional practice. They also investigate how this topic connects to mathematics, art, architecture, computer science, and the science of representation. Polyhedra and Beyond will help inspire scholars, researchers, professionals, and students of any of these disciplines to develop a more thorough understanding of polyhedra.
Contact Geometry of Slant Submanifolds
This book contains an up-to-date survey and self-contained chapters on contact slant submanifolds and geometry, authored by internationally renowned researchers. The notion of slant submanifolds was introduced by Prof. B.Y. Chen in 1990, and A. Lotta extended this notion in the framework of contact geometry in 1996. Numerous differential geometers have since obtained interesting results on contact slant submanifolds. The book gathers a wide range of topics such as warped product semi-slant submanifolds, slant submersions, semi-slant ξ┴ -, hemi-slant ξ┴ -Riemannian submersions, quasi hemi-slant submanifolds, slant submanifolds of metric f-manifolds, slant lightlike submanifolds, geometric inequalities for slant submanifolds, 3-slant submanifolds, and semi-slant submanifolds of almost paracontact manifolds. The book also includes interesting results on slant curves and magnetic curves, where the latter represents trajectories moving on a Riemannian manifold under the action of magnetic field. It presents detailed information on the most recent advances in the area, making it of much value to scientists, educators and graduate students.
Pure Metric Geometry
This book serves as an introductory asset for learning metric geometry by delivering an in-depth examination of key constructions and providing an analysis of universal spaces, injective spaces, the Gromov-Hausdorff convergence, and ultralimits. This book illustrates basic examples of domestic affairs of metric spaces, this includes Alexandrov geometry, geometric group theory, metric-measure spaces and optimal transport.Researchers in metric geometry will find this book appealing and helpful, in addition to graduate students in mathematics, and advanced undergraduate students in need of an introduction to metric geometry. Any previous knowledge of classical geometry, differential geometry, topology, and real analysis will be useful in understanding the presented topics.
Representation Theory and Algebraic Geometry
The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays. Based on the work of speakers and invited participants at the conference "Interactions Between Representation Theory and Algebraic Geometry", held at the University of Chicago, August 21-25, 2017, this volume illustrates the impact of their research and how it has shaped the development of various branches of mathematics through the use of D-modules, the affine Grassmannian, symplectic algebraic geometry, and other topics. All authors have been deeply influenced by their ideas and present here cutting-edge developments on modern topics. Chapters are organized around three distinct themes: Groups, algebras, categories, and representation theoryD-modules and perverse sheavesAnalogous varieties defined by quivers Representation Theory and Algebraic Geometry will be an ideal resource for researchers who work in the area, particularly those interested in exploring the impact of the Russian school.
Topics in Global Real Analytic Geometry
In the first two chapters we review the theory developped by Cartan, Whitney and Tognoli. Then Nullstellensatz is proved both for Stein algebras and for the algebra of real analytic functions on a C-analytic space. Here we find a relation between real Nullstellensatz and seventeenth Hilbert's problem for positive semidefinite analytic functions. Namely, a positive answer to Hilbert's problem implies a solution for the real Nullstellensatz more similar to the one for real polinomials. A chapter is devoted to the state of the art on this problem that is far from a complete answer. In the last chapter we deal with inequalities. We describe a class of semianalytic sets defined by countably many global real analytic functions that is stable under topological properties and under proper holomorphic maps between Stein spaces, that is, verifies a direct image theorem. A smaller class admits also a decomposition into irreducible components as it happens for semialgebraic sets. Duringthe redaction some proofs have been simplified with respect to the original ones.
An Introduction to Smooth Manifolds
Targeted to graduate students of mathematics, this book discusses major topics like the Lie group in the study of smooth manifolds. It is said that mathematics can be learned by solving problems and not only by just reading it. To serve this purpose, this book contains a sufficient number of examples and exercises after each section in every chapter. Some of the exercises are routine ones for the general understanding of topics. The book also contains hints to difficult exercises. Answers to all exercises are given at the end of each section. It also provides proofs of all theorems in a lucid manner. The only pre-requisites are good working knowledge of point-set topology and linear algebra.
Geometry of Derivation with Applications
Geometry of Derivation with Applications is the fifth work in a longstanding series of books on combinatorial geometry (Subplane Covered Nets, Foundations of Translation Planes, Handbook of Finite Translation Planes, and Combinatorics of Spreads and Parallelisms). Like its predecessors, this book will primarily deal with connections to the theory of derivable nets and translation planes in both the finite and infinite cases. Translation planes over non-commutative skewfields have not traditionally had a significant representation in incidence geometry, and derivable nets over skewfields have only been marginally understood. Both are deeply examined in this volume, while ideas of non-commutative algebra are also described in detail, with all the necessary background given a geometric treatment.The book builds upon over twenty years of work concerning combinatorial geometry, charted across four previous books and is suitable as a reference text for graduate students and researchers. It contains a variety of new ideas and generalizations of established work in finite affine geometry and is replete with examples and applications.
