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A Panoply of Polygons
 
Claudi Alsina Universitat Politècnica de Catalunya, Barcelona, Spain
Roger B. Nelsen Lewis & Clark College, Portland, OR
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-7184-2
Product Code:  DOL/58
List Price: $65.00
MAA Member Price: $48.75
AMS Member Price: $48.75
eBook ISBN:  978-1-4704-7294-8
Product Code:  DOL/58.E
List Price: $65.00
MAA Member Price: $48.75
AMS Member Price: $48.75
Softcover ISBN:  978-1-4704-7184-2
eBook: ISBN:  978-1-4704-7294-8
Product Code:  DOL/58.B
List Price: $130.00 $97.50
MAA Member Price: $97.50 $73.13
AMS Member Price: $97.50 $73.13
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A Panoply of Polygons
Claudi Alsina Universitat Politècnica de Catalunya, Barcelona, Spain
Roger B. Nelsen Lewis & Clark College, Portland, OR
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-7184-2
Product Code:  DOL/58
List Price: $65.00
MAA Member Price: $48.75
AMS Member Price: $48.75
eBook ISBN:  978-1-4704-7294-8
Product Code:  DOL/58.E
List Price: $65.00
MAA Member Price: $48.75
AMS Member Price: $48.75
Softcover ISBN:  978-1-4704-7184-2
eBook ISBN:  978-1-4704-7294-8
Product Code:  DOL/58.B
List Price: $130.00 $97.50
MAA Member Price: $97.50 $73.13
AMS Member Price: $97.50 $73.13
  • Book Details
     
     
    Dolciani Mathematical Expositions
    Volume: 582023; 267 pp
    MSC: Primary 51; 97

    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.

    Readership

    Undergraduate and graduate students and researchers interested in classical geometry.

  • Table of Contents
     
     
    • Chapters
    • Polygon basics
    • Pentagons
    • Hexagons
    • Heptagons
    • Octagons
    • Many-sided polygons
    • Miscellaneous classes of polygons
    • Polygonal numbers
    • Solutions to the challenges
  • Reviews
     
     
    • "A Panoply of Polygons" offers a panoply of reasons to be fascinated by its subject. If you love geometry, then this book will delight you. If you have forgotten how beautiful geometry is, then this book will remind you.

      Daniel Silver (University of South Alabama), Notices of the AMS
    • The reviewer went through this book with great pleasure, which is addressed to all those who love geometry; to all those who love beauty.

      Cătălin Barbu (Bačau)
    • The recent resolution to the long-standing question about the existence of aperiodic monotiles shows that there are deep questions one can ask about simple shapes. 'Panoply' is a more advanced book than you might expect if your last exposure to polygons was in a high school geometry class, though the book is accessible to readers without much more than a high school level background mathematics.

      'A Panoply of Polygons' is a fun read. The topics are nontrivial, but accessible, and can be read one or two pages at a time. It is not a textbook, at least not a conventional textbook, though it does have challenges at the end of each chapter that could be used as exercises. I think of it more as a book to keep on your nightstand, if, like the reviewer, you are the kind of person who keeps mathematics books on your nightstand.

      John D. Cook, MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 582023; 267 pp
MSC: Primary 51; 97

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.

Readership

Undergraduate and graduate students and researchers interested in classical geometry.

  • Chapters
  • Polygon basics
  • Pentagons
  • Hexagons
  • Heptagons
  • Octagons
  • Many-sided polygons
  • Miscellaneous classes of polygons
  • Polygonal numbers
  • Solutions to the challenges
  • "A Panoply of Polygons" offers a panoply of reasons to be fascinated by its subject. If you love geometry, then this book will delight you. If you have forgotten how beautiful geometry is, then this book will remind you.

    Daniel Silver (University of South Alabama), Notices of the AMS
  • The reviewer went through this book with great pleasure, which is addressed to all those who love geometry; to all those who love beauty.

    Cătălin Barbu (Bačau)
  • The recent resolution to the long-standing question about the existence of aperiodic monotiles shows that there are deep questions one can ask about simple shapes. 'Panoply' is a more advanced book than you might expect if your last exposure to polygons was in a high school geometry class, though the book is accessible to readers without much more than a high school level background mathematics.

    'A Panoply of Polygons' is a fun read. The topics are nontrivial, but accessible, and can be read one or two pages at a time. It is not a textbook, at least not a conventional textbook, though it does have challenges at the end of each chapter that could be used as exercises. I think of it more as a book to keep on your nightstand, if, like the reviewer, you are the kind of person who keeps mathematics books on your nightstand.

    John D. Cook, MAA Reviews
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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