Barycentric calculus in euclidean and hyperbolic geometry a comparative introduction.

• Main Author: Ungar, Abraham Albert
• Format: eBook Book
• Language: English
• Published: New Jersey ; London World Scientific Publishing Co. Pte. Ltd 2010; World Scientific; WORLD SCIENTIFIC; World Scientific Publishing
• Subjects: Calculus; Geometry, Hyperbolic; Geometry, Plane; Mathematical Physics; Mathematics; Pure Mathematics; Theoretical Physics; Triangle; Barycentric Calculus; Analogies with Classical Mechanics; Euclidean Geometry; Relativistic Center of Momentum; Hyperbolic Geometry; Triangle Excircles; Classical Center of Momentum; Barycentric Coordinates; Triangle Centers; Triangle Incircles; Analogies with Relativistic Mechanics
• ISBN: 981430493X; 9789814304931
• DOI: 10.1142/7740

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...

Table of Contents:

• Barycentric calculus in euclidean and hyperbolic geometry: a comparative introduction -- Preface -- Contents -- Chapter 1: Euclidean Barycentric Coordinates and the Classic Triangle Centers -- Chapter 2: Gyrovector Spaces and Cartesian Models of Hyperbolic Geometry -- Chapter 3: The Interplay of Einstein Addition and Vector Addition -- Chapter 4: Hyperbolic Barycentric Coordinates and Hyperbolic Triangle Centers -- Chapter 5: Hyperbolic Incircles and Excircles -- Chapter 6: Hyperbolic Tetrahedra -- Chapter 7: Comparative Patterns -- Notation And Special Symbols -- Bibliography -- Index