DESCRIPTION:

Binding: Paperback
Dewey Decimal Number: 516.2
EAN: 9780486462370
ISBN: 0486462374
Label: Dover Publications
Manufacturer: Dover Publications
Number Of Items: 1
Number Of Pages: 336
Publication Date: 2007-08-31
Publisher: Dover Publications
Studio: Dover Publications


SIMILAR ITEMS:

• College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (Dover Books on Mathematics)
• The Modern Geometry Of The Triangle
• Proof in Geometry: With "Mistakes in Geometric Proofs"
• Analytical Conics
• Kiselev's Geometry / Book I. Planimetry


CUSTOMER REVIEWS:

Customer Rating:
Summary: A Classic on Euclidean geometry
Comment: Recently Dover has reissued two classics on Euclidean geometry, College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle (Dover Books on Mathematics) and this book. Both books were originally issued in the first half of the 20th century and both were aimed at a college level audience. Both of them also have a considerable amount of so called triangle geometry. As triangle geometry has seen a large upsurge the last years there is certainly a need for an English book that gives an overview of the subject. These books are useful in this respect but are out of date. Until a modern treatment of the subject will be available, these two books and the resources on the www will have to do. Altshiller Courts' book has a great set of exercises that can be used as a training ground for geometric problem solving. The problems in Johnsons' book mostly ask for proofs of theorems that are ommited in the text (that's why I give 4 stars). If you are interested in the subject, buy both, its certainly value for money.

The book assumes that you are familiar with simple geometrical concepts like congruence of triangles, parallelograms, circles and the most elementary theorems and constructions as can be found in Kiselev's book Kiselev's Geometry / Book I. Planimetry.

The table of contents:

I Introduction
Prerequisites
Points at infinity
Notation
Directed angles

II Similar Figures
Homothetic figures
Centers of similitude of two circles
Similar figures in general

III Coaxal circles and inversions
The radical axis
Coaxal circles
Inversions

IV Triangles and Polygons
Ratios in the triangle
Quadrangles and quadrilaterals
The theorem of Ptolemy
Triangle and quadrangle theorems
Polygon theorems and exercises
Theorems concerning areas

V Geometry of Circles
The power theorem of Casey
Circles of antisimilitude
Poles and polars
Stereographic projection

VI Tangent Circles
Circles tangent to two circles
Steiner chains; the arbelos
The problem of Apollonius
Four circles touching a circle

VII The theorem of Miquel
The Miquel theorem
Pedal triangles and circles; Simson lines

VII Theorems of Ceva and Menelaos
Theorems of Ceva and Menelaos; applications
Isogonal conjugates

IX Three Notable Points
Fundamental properties of orthocenter and circumcenter
The orthocentric system
Properties of the median point
The polar circle

X Inscribed and Escribed Circles
Fundamental properties
Algebraic formulas; principle of transformation

XI The nine point circle
Properties of the nine point circle
The theorem of Feuerbach
Further properties of Simson lines

XII Symmedian Point and Other Notable Points
Symmedians and the symmedian point
The isogonic centres
Nagel point, Spieker circle, Fuhrmann circle

XIII Triangles in Perspective
The theorem of Desargues
The theorems of Pascal and Brianchon

XIV Pedal Triangles and Circles
Pedal triangles and circles of a quadrangle
Fontené's theorems; the theorem of Feuerbach
The orthopole

XV Shorter Topics
Statical theorems: center of gravity, resultant of vectors
The cyclic quadrangle and its orthocenters
The theorem of Morley
Circles of Droz-Farny
Miscellaneous exercises

XVI The Brocard Configuration
The Brocard points and their properties
The Tucker circles
The Brocard triangles and the Brocard circle
Steiner point and Tarry point
Related triangles

XVII Equibrocardal Triangles
The Neuberg circles
Vertical projection of triangles
Circles of Appolonius and isodynamic points
The circles of Schoute
Generalizations of Brocard geometry

XVIII Three Similar Figures
Similar figures on the sides of a triangle
Three similar figures in general

Index

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