Geometry Theorems and Constructions

ISBN-10: 0130871214
ISBN-13: 9780130871213
Edition: 2001
List price: $117.80 Buy it from $9.84
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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  More...

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Book details

List price: $117.80
Copyright year: 2001
Publisher: Prentice Hall PTR
Publication date: 10/6/2000
Binding: Hardcover
Pages: 224
Size: 7.00" wide x 9.25" long x 0.50" tall
Weight: 1.452
Language: English

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 to focus more on learning to do proofs by keeping the material less abstract. For readers pursuing a career in mathematics.

(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 Poincar� Disk
The AAA Theorem in Hyperbolic Geometry
Geometry and the Physical Universe

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