EXPLORATIONS IN GEOMETRY

By: SHAWYER BRUCE

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Paperback | 18 March 2010

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320 Pages

Dimensions(cm)
22.86 x 15.24 x 1.7

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This book covers the basic topics in geometry (including trigonometry) that are accessible and valuable to senior high school and university students. It also includes materials that are very useful for problem solving in mathematical competitions, from relatively easy to advanced levels, including the International Mathematical Olympiad.

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Basic Euclidean Geometry	p. 1
Triangles	p. 1
Similar Triangles	p. 2
Congruent Triangles	p. 3
Quadrilaterals	p. 4
Polygons	p. 5
Circles and Angles	p. 6
Cyclic Quadrilaterals	p. 11
Intersecting Chords	p. 14
Inversion	p. 16
Reflection in a line	p. 16
Inversion in a circle	p. 16
Trigonometry	p. 21
Basic Definitions	p. 21
Complementary Angles	p. 22
Supplementary Angles	p. 23
Extensions	p. 24
Addition Formulae	p. 26
Double Angle Formulae	p. 27
Half Angle Formulae	p. 28
The Sine Rule	p. 30
The Cosine Rule	p. 32
The Area of a Triangle	p. 34
Inverse Trigonometric Functions	p. 35
The Sine and Cosine Functions	p. 35
The Tangent Function	p. 38
De Moivre's Theorem	p. 39
Roots of Unity and Euler's Formula	p. 40
Hyperbolic Functions	p. 44
Inverse Hyperbolic Functions	p. 45
Concurrency and Collinearity	p. 49
Menelaus' Theorem	p. 49
Ceva's Theorem	p. 52
Particular Concurrency Results	p. 53
Medians	p. 53
Altitudes	p. 54
Perpendicular Bisectors of the Sides	p. 55
Interior Angle Bisectors	p. 56
Exterior Angle Bisectors	p. 57
The Gergonne Point	p. 58
The Wallace-Simson Line	p. 59
The Nine Point Circle	p. 60
The Euler Line	p. 63
The Miquel Point	p. 65
Joshua Klehr's Theorem and its Extensions	p. 66
First extension	p. 67
Second extension	p. 74
Circumcircle, Inradius and Semiperimeter Formulae	p. 77
Semi-perimeter Formulae	p. 77
Half Angle Formulae	p. 79
In-radius Formulae	p. 81
Escribed Circles	p. 82
Conic Sections	p. 85
Review	p. 85
Basic Definitions	p. 85
The Parabola	p. 86
The Ellipse	p. 87
The Hyperbola	p. 88
Parametric Equations	p. 92
Parabolas	p. 92
Ellipses	p. 92
Hyperbolas	p. 93
General Second Degree Equations	p. 93
Constructions	p. 95
Elementary Constructions	p. 95
Bisection of a line segment	p. 95
Bisection of an angle	p. 97
Drawing a perpendicular to a line	p. 98
Drawing a parallel line	p. 99
Trisection of a line segment	p. 99
Regular Polygons	p. 100
Three Sides - equilateral triangle	p. 101
Four Sides - square	p. 101
Five Sides - regular pentagon	p. 102
Seventeen Sides - regular 17-gon	p. 104
Other polygons	p. 105
The Carpenter's "Theorem"	p. 106
The theory of the Carpenter's "Theorem"	p. 107
The Draughtsman's "Theorem"	p. 107
Theory of the Draughtsman's "Theorem"	p. 108
The Master Carpenter's "Theorem"	p. 109
Comparison of the three constructions	p. 110
Real Numbers	p. 111
Integral Multiples	p. 111
Rational Multiples	p. 111
Irrational Multiples	p. 111
The Broken Chord Theorem	p. 115
Cleavers and Splitters	p. 119
Cleavers	p. 119
Splitters	p. 121
Collinearity	p. 122
Remarkable Bisections	p. 125
Miscellaneous Problems	p. 129
Problems from Crux Mathematicorum with Mathematical Mayhem	p. 152
Problems with Solutions	p. 157
Problems from Crux Mathematicorum with Mathematical Mayhem	p. 290
Index	p. 305
Table of Contents provided by Ingram. All Rights Reserved.

EXPLORATIONS IN GEOMETRY

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Hardcover

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Grades 6 - 8

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The Maths Book

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Calculus

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Grade 6 Geometry and Measurement

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Grade 1 Geometry & Measurement

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Crocheting Adventures with Hyperbolic Planes

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Introduction to Lie Algebras

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The Practice of Algebraic Curves

A Second Course in Algebraic Geometry

Introduction to Lie Algebras

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A Second Course in Algebraic Geometry

Saturated Fusion Systems on $p$-Groups of Maximal Class

Steady Gradient Kahler-Ricci Solitons on Crepant Resolutions of Calabi-Yau Cones

$G$-Global Homotopy Theory and Algebraic $K$-Theory

Para-HyperKahler Geometry of the Deformation Space of Maximal Globally Hyperbolic Anti-de Sitter Three-Manifolds

The Dynamics and Geometry of Semi-Hyperbolic Rational Semigroups

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