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.

The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. This book is suitable as a text or for self-study.

Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.

For students who have completed an introductory calculus course in high school, this textbook provides a thorough grounding in many subsequent single variable calculus topics. Beginning with a review of some high school calculus content, it proceeds to more advanced material including integration techniques, applications of the definite integral, separable and linear differential equations, hyperbolic functions, parametric equations and polar coordinates, L'Hopital's rule and improper integrals, continuous probability models, and infinite series. Each chapter concludes with several 'Explorations', extended discovery investigations to supplement that chapter's material and enhance the learning experience. The text is ideal as the basis of a course for prospective majors in the STEM disciplines (science, technology, engineering, and mathematics). A one-term course based on this text provides students with a solid foundation in single variable calculus and prepares them for the next course in college-level mathematics, be it multivariable calculus, linear algebra, discrete mathematics or statistics.

Proofs without words are generally pictures or diagrams that help the reader see why a particular mathematical statement may be true, and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: Geometry and algebra; Trigonometry, calculus and analytic geometry; Inequalities; Integer sums; and Sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.

Dieses Buch handelt von 20 geometrischen Figuren (Icons), die eine wichtige Rolle bei der Veranschaulichung mathematischer Beweise spielen. Alsina und Nelsen untersuchen die Mathematik, die hinter diesen Figuren steckt und die sich aus ihnen ableiten lasst. Jedem in diesem Buch behandelten Icons ist ein eigenes Kapitel gewidmet, in dem sein Alltagsbezug, seine wesentlichen mathematischen Eigenschaften sowie seine Bedeutung fur visuelle Beweise vieler mathematischer Satze betont werden. Diese Satze umfassen unter anderem auch klassische Ergebnisse aus der ebenen Geometrie, Eigenschaften der naturlichen Zahlen, Mittelwerte und Ungleichungen, Beziehungen zwischen Winkelfunktionen, Satze aus der Differenzial- und Integralrechnung sowie Ratsel aus dem Bereich der Unterhaltungsmathematik. Daruber hinaus enthalt jedes Kapitel eine Auswahl an Aufgaben, anhand derer die Leser weitere Eigenschaften und Anwendungen der Diagramme erkunden koennen. Das Buch ist fur alle geschrieben, die Freude an der Mathematik haben; Lehrkrafte und Dozenten der Mathematik werden in diesem Buch sehr nutzliche Beispiele fur Problemloesungen sowie umfangreiches Unterrichts- und Seminarmaterial zu Beweisen und mathematischer Argumentation finden.

Sie ratseln gerne und haben ein Faible fur Mathematik? Mit den Grafiken dieses Buches finden Sie einen eleganten Zugang zu ausgewahlten mathematischen Kostbarkeiten. Die gesammelten Illustrationen sind nicht nur schoen anzusehen, sie helfen auch beim Verstehen von Formeln und bebildern erstaunliche Zusammenhange. Beweise ohne Worte animieren zum selbststandigen Nachdenken uber Mathematik und geben Anstoss zu vollstandigen Beweisen. Diese Sammlung bietet Beispiele auf allen Niveaus aus unterschiedlichen Disziplinen: Sie lernen Spannendes uber Geometrie, Kombinatorik, Arithmetik und Analysis kennen. Dieses Potpourri von bildlichen Beweisen visualisiert kleine Knobeleien und bekannte Schulmathematik in neuem Gewande, aber auch anspruchsvolle Mathematik, wie sie im Studium auftritt. Und Sie bekommen Lust, sich selbst Gedanken fur weitere Beweise ohne Worte zu machen.

Satze und ihre Beweise bilden das Herz der Mathematik.

Diese Sammlung bezaubernder Beweise, verbluffender Argumente und uberzeugender bildlicher Darstellungen ladt den Leser ein, sich an der Schonheit der Mathematik zu erfreuen, seine Entdeckungen mit anderen zu teilen und bei dem Finden neuer Beweise mitzumachen.

Das Buch umfasst folgende Themen: naturliche Zahlen, besondere reelle Zahlen, Punkte in der Ebene, Dreiecke, Quadrate, andere Vielecke, Kurven, Ungleichungen, ebene Parkettierungen, Origami, Beweise mit Farbungen, dreidimensionale Geometrie, usw.

Jedes Kapitel endet mit einigen Aufgaben, die den Leser in die Kunst des Auffindens vonbezaubernden Beweisen einbezieht. Es gibt insgesamt uber 130 solcher Aufgaben. "

The authors present twenty icons of mathematics, that is, geometrical shapes such as the right triangle, the Venn diagram, and the yang and yin symbol and explore mathematical results associated with them. As with their previous books (Charming Proofs, When Less is More, Math Made Visual) proofs are visual whenever possible. The results require no more than high-school mathematics to appreciate and many of them will be new even to experienced readers. Besides theorems and proofs, the book contains many illustrations and it gives connections of the icons to the world outside of mathematics. There are also problems at the end of each chapter, with solutions provided in an appendix. The book could be used by students in courses in problem solving, mathematical reasoning, or mathematics for the liberal arts. It could also be read with pleasure by professional mathematicians, as it was by the members of the Dolciani editorial board, who unanimously recommend its publication.

A Cornucopia of Quadrilaterals collects and organizes hundreds of beautiful and surprising results about four-sided figures--for example, that the midpoints of the sides of any quadrilateral are the vertices of a parallelogram, or that in a convex quadrilateral (not a parallelogram) the line through the midpoints of the diagonals (the Newton line) is equidistant from opposite vertices, or that, if your quadrilateral has an inscribed circle, its center lies on the Newton line. There are results dating back to Euclid: the side-lengths of a pentagon, a hexagon, and a decagon inscribed in a circle can be assembled into a right triangle (the proof uses a quadrilateral and circumscribing circle); and results dating to Erdos: from any point in a triangle the sum of the distances to the vertices is at least twice as large as the sum of the distances to the sides. The book is suitable for serious study, but it equally rewards the reader who dips in randomly. It contains hundreds of challenging four-sided problems. Instructors of number theory, combinatorics, analysis, and geometry will find examples and problems to enrich their courses. The authors have carefully and skillfully organized the presentation into a variety of themes so the chapters flow seamlessly in a coherent narrative journey through the landscape of quadrilaterals. The authors' exposition is beautifully clear and compelling and is accessible to anyone with a high school background in geometry.

Nuggets of Number Theory will attract fans of visual thinking, number theory, and surprising connections. This book contains hundreds of visual explanations of results from elementary number theory. Figurate numbers and Pythagorean triples feature prominently, of course, but there are also proofs of Fermat's Little and Wilson's Theorems. Fibonacci and perfect numbers, Pell's equation, and continued fractions all find visual representation in this charming collection. It will be a rich source of visual inspiration for anyone teaching, or learning, number theory and will provide endless pleasure to those interested in looking at number theory with new eyes. Author Roger Nelsen is a long-time contributor of ``Proofs Without Words'' in the MAA's Mathematics Magazine and College Mathematics Journal. This is his twelfth book with MAA Press.

The Calculus Collection is a useful resource for everyone who teaches calculus, in secondary school or in a college or university. It consists of 123 articles selected by a panel of veteran secondary school teachers. The articles focus on engaging students who are meeting the core ideas of calculus for the first time and who are interested in a deeper understanding of single-variable calculus. The Calculus Collection is filled with insights, alternative explanations of difficult ideas, and suggestions for how to take a standard problem and open it up to the rich mathematical explorations available when you encourage students to dig a little deeper. Some of the articles reflect an enthusiasm for bringing calculators and computers into the classroom, while others consciously address themes from the calculus reform movement. But most of the articles are simply interesting and timeless explorations of the mathematics encountered in a first course in calculus.