Geometry revisited / by H.S.M. Coxeter and S.L. Greitzer.

Format:

Book

Author/Creator:

Coxeter, H. S. M. (Harold Scott Macdonald), 1907-2003.

Contributor:

Greitzer, Samuel L.

Series:

New mathematical library ; 19.

Anneli Lax New Mathematical Library ; 19

Language:

English

Subjects (All):

Geometry.

Mathematics.

Physical Description:

1 online resource (xiv, 193 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Washington, DC : Mathematical Association of America, 1967.

Language Note:

English

Summary:

Among the many beautiful and nontrivial theorems in geometry found here are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.

Contents:

""Front Cover""; ""Geometry Revisited""; ""Copyright Page""; ""Contents""; ""Preface""; ""Chapter 1. Points and Lines Connected with a Triangle""; ""1.1 The extended Law of Sines""; ""1.2 Ceva�s theorem""; ""1.3 Points of interest""; ""1.4 The incircle and excircles""; ""1.5 The Steiner-Lehmus theorem""; ""1.6 The orthic triangle""; ""1.7 The medial triangle and Euler line""; ""1.8 The nine-point Circle""; ""1.9 Pedal triangles""; ""Chapter 2. Some Properties of Circles""; ""2.1 The power of a point with respect to a circle""; ""2.2 The radical axis of two circles""; ""2.3 Coaxal circles""

""2.4 More on the altitudes and orthocenter of a triangle""""2.5 Simson lines""; ""2.6 Ptolemy�s theorem and its extension""; ""2.7 More on Simson lines""; ""2.8 The Butterfly""; ""2.9 Morley�s theorem""; ""Chapter 3. Collinearity and Concurrence""; ""3.1 Quadrangles; Varignon�s theorem""; ""3.2 Cyclic quadrangles; Brahmagupta�s formula""; ""3.3 Napoleon triangles""; ""3.4 Menelaus�s theorem""; ""3.5 Pappus�s theorem""; ""3.6 Perspective triangles; Desargues�s theorem""; ""3.7 Hexagons""; ""3.8 Pascal�s theorem""; ""3.9 Brianchon�s theorem""

""Chapter 4. Transformations""""4.1 Translation""; ""4.2 Rotation""; ""4.3 Half-turn""; ""4.4 Reflection""; ""4.5 Fagnano�s problem""; ""4.6 The three jug problem""; ""4.7 Dilatation""; ""4.8 Spiral similarity""; ""4.9 A genealogy of transformations""; ""Chapter 5. An Introduction to Inversive Geometry""; ""5.1 Separation""; ""5.2 Cross ratio""; ""5.3 Inversion""; ""5.4 The inversive plane""; ""5.5 Orthogonality""; ""5.6 Feuerbach�s theorem""; ""5.7 Coaxal circles""; ""5.8 Inversive distance""; ""5.9 Hyperbolic functions""; ""Chapter 6. An Introduction to Projective Geometry""

""6.1 Reciprocation""""6.2 The polar circle of a triangle""; ""6.3 Conics""; ""6.4 Focus and directrix""; ""6.5 The projective plane""; ""6.6 Central conics""; ""6.7 Stereographic and gnomonic projection""; ""Hints and Answers to Exercises""; ""References""; ""Glossary""; ""Index""; ""Back Cover""

Notes:

Title from publisher's bibliographic system (viewed on 31 May 2016).

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9780883859346

0883859343

OCLC:

929120235