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.
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Collects and organises hundreds of beautiful and surprising results about four-sided figures. The book contains hundreds of challenging four-sided problems. Instructors of number theory, combinatorics, analysis, and geometry will find examples and problems to enrich their courses.
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  • Simple quadrilaterals
  • Quadrilaterals and their circles
  • Diagonals of quadrilaterals
  • Properties of trapezoids
  • Applications of trapezoids
  • Garfield trapezoids and rectangles
  • Parallelograms
  • Rectangles
  • Squares
  • Special quadrilaterals
  • Quadrilateral numbers
  • Solutions to the Challenges
  • A quadrilateral glossary
  • Credits and permissions
  • Bibliography
  • Index.
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Produktdetaljer

ISBN
9781470453121
Publisert
2020-02-28
Utgiver
Vendor
American Mathematical Society
Vekt
577 gr
Høyde
229 mm
Bredde
153 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
304

Biographical note

Claudi Alsina, Universitat Politecnica de Catalunya, Barcelona, Spain

Roger B. Nelsen, Lewis & Clark College, Portland, OR