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A Cornucopia of Quadrilaterals (Hardcover)
Loot Price: R1,519
Discovery Miles 15 190
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A Cornucopia of Quadrilaterals (Hardcover)
Series: Dolciani Mathematical Expositions
Expected to ship within 12 - 17 working days
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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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