Geometry Theorems and Constructions

Name: Geometry Theorems and Constructions
Price: 15.35 USD
Availability: InStock
ISBN: 9780130871213

ISBN-10: 0130871214

ISBN-13: 9780130871213

Edition: 2001

Authors: Allan Berele, Jerry Goldman

List price: $119.99

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Description:

College Geometry offers readers a deep understanding of the basic results in plane geometry and how they are used. Its unique coverage helps readers master Euclidean geometry, in preparation for non- Euclidean geometry. Focus on plane Euclidean geometry, reviewing high school level geometry and coverage of more advanced topics equips readers with a thorough understanding of Euclidean geometry, needed in order to understand non-Euclidean geometry. Coverage of Spherical Geometry in preparation for introduction of non-Euclidean geometry. A strong emphasis on proofs is provided, presented in various levels of difficulty and phrased in the manner of present-day mathematicians, helping the reader…

Book details

List price: $119.99
Copyright year: 2001
Publisher: Prentice Hall PTR
Publication date: 10/6/2000
Binding: Hardcover
Pages: 256
Size: 7.00" wide x 9.25" long x 0.50" tall
Weight: 1.188
Language: English



(NOTE:Each chapter concludes with a Chapter Summary.) 0<$$$>


Notation and Conventions


Notation


Constructions



Congruent Triangles


The Three Theorems


Proofs of the Three Theorems


Applications to Constructions


Applications to Inequalities



Parallel Lines


Existence and Uniqueness


Applications


Distance between Parallel Lines



Area


Area of Rectangles and Triangles


The Pythagorean Theorem


Area of Triangles


Cutting and Pasting



Similar Triangles


The Three Theorems


Applications to Constructions



Circles


Circles and Tangents


Arcs and Angles


Applications to Constructions


Application to Queen Dido's Problem


More on Arcs and Angles



Regular Polygons


Constructibility


In the Footsteps of Archimedes



Triangles and Circles


Circumcircles


A Theorem of Brahmagupta


Inscribed Circles


An Old Chestnut (the Steiner-Lehmus Theorem.) Enscribed Circles


Euler's Theorem



Medians


Center of Gravity


Length Formulas


Complementary and Anticomplementary Triangles



Altitudes


The Orthocenter


Fagnano's Problem


The Euler Line


The Nine-Point Circle



Miscellaneous Results about Triangles


Ceva's Theorem


Applications of Ceva's Theorem


The Fermat Point


Properties of the Fermat Point



Constructions with Indirect Elements


Constructions with Indirect Elements



Solid Geometry


Lines and Planes in Space


Dihedral Angles


Projections


Trihedral Angles



Combinatorial Theorems in Geometry


The Triangulation Lemma


Euler's Theorem


Platonic Solids


Pick's Theorem



Spherical Geometry


Spheres and Great Circles


Spherical Triangles


Polar Triangles


Congruence Theorems for Triangles


Areas of Spherical Triangles


A Non-Euclidean Model



Models for Hyperbolic Geometry


Absolute Geometry


The Klein-Beltrami Disk


The Poincarï¿½ Disk


The AAA Theorem in Hyperbolic Geometry


Geometry and the Physical Universe