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Barycentric calculus in Euclidean an...

Ungar, Abraham A.

Barycentric calculus in Euclidean and hyperbolic geometrya comparative introduction /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Barycentric calculus in Euclidean and hyperbolic geometryAbraham Albert Ungar.
Reminder of title:	a comparative introduction /
Author:	Ungar, Abraham A.
Published:	Singapore ;World Scientific,c2010.
Description:	1 online resource (xiv, 344 p.) :ill.
Subject:	Geometry, Plane.
Online resource:	http://www.worldscientific.com/worldscibooks/10.1142/7740#t=toc
ISBN:	9789814304948 (electronic bk.)

Barycentric calculus in Euclidean and hyperbolic geometrya comparative introduction /
Ungar, Abraham A.

Barycentric calculus in Euclidean and hyperbolic geometrya comparative introduction /[electronic resource] :Abraham Albert Ungar. - Singapore ;World Scientific,c2010. - 1 online resource (xiv, 344 p.) :ill.

Includes bibliographical references and index.

The word barycentric is derived from the Greek word barys (heavy), and refers to center of gravity. Barycentric calculus is a method of treating geometry by considering a point as the center of gravity of certain other points to which weights are ascribed. Hence, in particular, barycentric calculus provides excellent insight into triangle centers. This unique book on barycentric calculus in Euclidean and hyperbolic geometry provides an introduction to the fascinating and beautiful subject of novel triangle centers in hyperbolic geometry along with analogies they share with familiar triangle centers in Euclidean geometry. As such, the book uncovers magnificent unifying notions that Euclidean and hyperbolic triangle centers share. In his earlier books the author adopted Cartesian coordinates, trigonometry and vector algebra for use in hyperbolic geometry that is fully analogous to the common use of Cartesian coordinates, trigonometry and vector algebra in Euclidean geometry. As a result, powerful tools that are commonly available in Euclidean geometry became available in hyperbolic geometry as well, enabling one to explore hyperbolic geometry in novel ways. In particular, this new book establishes hyperbolic barycentric coordinates that are used to determine various hyperbolic triangle centers just as Euclidean barycentric coordinates are commonly used to determine various Euclidean triangle centers. The hunt for Euclidean triangle centers is an old tradition in Euclidean geometry, resulting in a repertoire of more than three thousand triangle centers that are known by their barycentric coordinate representations. The aim of this book is to initiate a fully analogous hunt for hyperbolic triangle centers that will broaden the repertoire of hyperbolic triangle centers provided here.

ISBN: 9789814304948 (electronic bk.)Subjects--Topical Terms:

275746
Geometry, Plane.

LC Class. No.: QA455 / .U54 2010eb

Dewey Class. No.: 516.22

Barycentric calculus in Euclidean and hyperbolic geometrya comparative introduction /
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300 $a 1 online resource (xiv, 344 p.) : $b ill.
504 $a Includes bibliographical references and index.
520 $a The word barycentric is derived from the Greek word barys (heavy), and refers to center of gravity. Barycentric calculus is a method of treating geometry by considering a point as the center of gravity of certain other points to which weights are ascribed. Hence, in particular, barycentric calculus provides excellent insight into triangle centers. This unique book on barycentric calculus in Euclidean and hyperbolic geometry provides an introduction to the fascinating and beautiful subject of novel triangle centers in hyperbolic geometry along with analogies they share with familiar triangle centers in Euclidean geometry. As such, the book uncovers magnificent unifying notions that Euclidean and hyperbolic triangle centers share. In his earlier books the author adopted Cartesian coordinates, trigonometry and vector algebra for use in hyperbolic geometry that is fully analogous to the common use of Cartesian coordinates, trigonometry and vector algebra in Euclidean geometry. As a result, powerful tools that are commonly available in Euclidean geometry became available in hyperbolic geometry as well, enabling one to explore hyperbolic geometry in novel ways. In particular, this new book establishes hyperbolic barycentric coordinates that are used to determine various hyperbolic triangle centers just as Euclidean barycentric coordinates are commonly used to determine various Euclidean triangle centers. The hunt for Euclidean triangle centers is an old tradition in Euclidean geometry, resulting in a repertoire of more than three thousand triangle centers that are known by their barycentric coordinate representations. The aim of this book is to initiate a fully analogous hunt for hyperbolic triangle centers that will broaden the repertoire of hyperbolic triangle centers provided here.
588 $a Description based on print version record.
650 0 $a Geometry, Plane. $3 275746
650 0 $a Geometry, Hyperbolic. $3 190984
650 0 $a Triangle. $3 484125
650 0 $a Calculus. $3 183091
856 4 0 $u http://www.worldscientific.com/worldscibooks/10.1142/7740#t=toc