Advanced Euclidian Geometry: Excursions for Students and Teachers

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Springer Science & Business Media, 12.07.2002 г. - 254 страници
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Advanced Euclidean Geometry provides a thorough review of the essentials of high school geometry  and then expands those concepts to advanced Euclidean geometry, to give teachers more confidence in guiding student explorations and questions.

The text contains hundreds of illustrations created in The Geometer's Sketchpad Dynamic Geometry® software. It is packaged with a CD-ROM containing over 100 interactive sketches using SketchpadTM (assumes that the user has access to the program).

 

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Съдържание

LEARNING FROM GEOMETRIC FALLACIES
11
COMMON NOMENCLATURE
18
CONCURRENCY OF LINES IN A TRIANGLE
22
INTRODUCTION
23
CEVAS THEOREM
25
APPLICATIONS OF CEVAS THEOREM
30
THE GERGONNE POINT
34
COLLINEARITY OF POINTS
40
QUADRILATERALS
116
CENTERS OF A QUADRILATERAL
119
CYCLIC QUADRILATERALS
123
PTOLEMYS THEOREM
128
APPLICATIONS OF PTOLEMYS THEOREM
131
EQUICIRCLES
140
POINTS OF TANGENCY
141
EQUIRADII
146

DUALITY
41
MENELAUSS THEOREM
43
APPLICATIONS OF MENELAUSS THEOREM
46
DESARGUESS THEOREM
49
PASCALS THEOREM
52
BRIANCHONS THEOREM
55
PAPPUSS THEOREM
58
THE SIMSON LINE
59
RADICAL AXES
66
SOME SYMMETRIC POINTS IN A TRIANGLE
75
INTRODUCTION
76
EQUIANGULAR POINT
77
PROPERTY OF EQUILATERAL TRIANGLES
80
A MINIMUM DISTANCE POINT
81
MORE TRIANGLE PROPERTIES
85
INTRODUCTION
86
STEWARTS THEOREM
96
MIQUELS THEOREM
100
MEDIANS
106
THE NINEPOINT CIRCLE
155
TO THE NINEPOINT CIRCLE
156
ATTITUDES
161
THE NINEPOINT CIRCLE REVISITED
166
TRIANGLE CONSTRUCTIONS
170
INTRODUCTION
171
SELECTED CONSTRUCTIONS
178
CIRCLE CONSTRUCTIONS
198
INTRODUCTION
199
THE GOLDEN SECTION AND FIBONACCI NUMBERS
213
THE GOLDEN RATIO
214
FIBONACCI NUMBERS
218
LUCAS NUMBERS
224
FIBONACCI NUMBERS AND LUCAS NUMBERS IN GEOMETRY
228
THE GOLDEN RECTANGLE REVISITED
233
THE GOLDEN TRIANGLE
238
INDEX
247
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