Topics in elementary geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Dutch |
| Veröffentlicht: |
New York, NY
Springer
2008
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Angekündigt u.d.T.: Bottema, Oene: Selected topics in elementary geometry |
| Beschreibung: | XII, 142 S. graph. Darst. |
| ISBN: | 9780387781303 9780387781310 |
Internformat
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| 300 | |a XII, 142 S. |b graph. Darst. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text |
Contents
Foreword VII
Preface to the Second Edition IX
1 The Pythagorean Theorem 1
2 Ceva's Theorem 7
3 Perpendicular Bisectors; Concurrence 13
4 The Nine-Point Circle and Euler Line 19
5 The Taylor Circle 23
6 Coordinate Systems with Respect to a Triangle 25
7 The Area of a Triangle as a Function of the Barycentric
Coordinates of Its Vertices 29
8 The Distances from a Point to the Vertices of a Triangle. 33
9 The Simson Line 39
10 Morley's Triangle 43
11 Inequalities in a Triangle 47
12 The Mixed Area of Two Parallel Polygons 51
13 The Isoperimetric Inequality 57
14 Poncelet Polygons 65
XII Contents
15 A Closure Problem for Triangles 73
16 A Class of Special Triangles 77
17 Two Unusual Conditions for a Triangle 81
18 A Counterpart for the Euler Line 83
19 Menelaus's Theorem; Cross-Ratios and Reciprocation 85
20 The Theorems of Desargues, Pappus, and Pascal 91
21 Inversion 99
22 The Theorems of Ptolemy and Casey 103
23 Pedal Triangles; Brocard Points 107
24 Isogonal Conjugation; the Symmedian Point Ill
25 Isotomic Conjugation 117
26 Triangles with Two Equal Angle Bisectors 119
27 The Inscribed Triangle with the Smallest Perimeter; the
Fermat Point 123
Appendix: Remarks and Hints 127
Bibliography 133
Index 139 |
| adam_txt |
Contents
Foreword VII
Preface to the Second Edition IX
1 The Pythagorean Theorem 1
2 Ceva's Theorem 7
3 Perpendicular Bisectors; Concurrence 13
4 The Nine-Point Circle and Euler Line 19
5 The Taylor Circle 23
6 Coordinate Systems with Respect to a Triangle 25
7 The Area of a Triangle as a Function of the Barycentric
Coordinates of Its Vertices 29
8 The Distances from a Point to the Vertices of a Triangle. 33
9 The Simson Line 39
10 Morley's Triangle 43
11 Inequalities in a Triangle 47
12 The Mixed Area of Two Parallel Polygons 51
13 The Isoperimetric Inequality 57
14 Poncelet Polygons 65
XII Contents
15 A Closure Problem for Triangles 73
16 A Class of Special Triangles 77
17 Two Unusual Conditions for a Triangle 81
18 A Counterpart for the Euler Line 83
19 Menelaus's Theorem; Cross-Ratios and Reciprocation 85
20 The Theorems of Desargues, Pappus, and Pascal 91
21 Inversion 99
22 The Theorems of Ptolemy and Casey 103
23 Pedal Triangles; Brocard Points 107
24 Isogonal Conjugation; the Symmedian Point Ill
25 Isotomic Conjugation 117
26 Triangles with Two Equal Angle Bisectors 119
27 The Inscribed Triangle with the Smallest Perimeter; the
Fermat Point 123
Appendix: Remarks and Hints 127
Bibliography 133
Index 139 |
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| discipline | Mathematik |
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| edition | 2. ed. |
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| index_date | 2024-07-02T21:39:32Z |
| indexdate | 2024-07-20T09:47:19Z |
| institution | BVB |
| isbn | 9780387781303 9780387781310 |
| language | English Dutch |
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