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Hardcover ISBN:  9781470453121 
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Hardcover ISBN:  9781470453121 
Product Code:  DOL/55 
List Price:  $59.00 
MAA Member Price:  $44.25 
AMS Member Price:  $44.25 
eBook ISBN:  9781470454654 
Product Code:  DOL/55.E 
List Price:  $59.00 
MAA Member Price:  $44.25 
AMS Member Price:  $44.25 
Hardcover ISBN:  9781470453121 
eBook ISBN:  9781470454654 
Product Code:  DOL/55.B 
List Price:  $118.00 $88.50 
MAA Member Price:  $88.50 $66.38 
AMS Member Price:  $88.50 $66.38 

Book DetailsDolciani Mathematical ExpositionsVolume: 55; 2020; 304 ppMSC: Primary 51;
A Cornucopia of Quadrilaterals collects and organizes hundreds of beautiful and surprising results about foursided 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 sidelengths 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 Erdős: 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 foursided 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.ReadershipUndergraduate and graduate students interested in geometry.

Table of Contents

Chapters

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


Additional Material

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A Cornucopia of Quadrilaterals collects and organizes hundreds of beautiful and surprising results about foursided 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 sidelengths 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 Erdős: 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 foursided 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.
Undergraduate and graduate students interested in geometry.

Chapters

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