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Books > Science & Mathematics > Mathematics > Geometry > Non-Euclidean geometry
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Barycentric Calculus In Euclidean And Hyperbolic Geometry: A Comparative Introduction (Hardcover)
Loot Price: R3,134
Discovery Miles 31 340
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Barycentric Calculus In Euclidean And Hyperbolic Geometry: A Comparative Introduction (Hardcover)
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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.
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