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El. knyga: Plain Plane Geometry

(London School Of Economics, Uk)
  • Formatas: 288 pages
  • Išleidimo metai: 07-Dec-2015
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • Kalba: eng
  • ISBN-13: 9789814740463
Kitos knygos pagal šią temą:
  • Formatas: 288 pages
  • Išleidimo metai: 07-Dec-2015
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • Kalba: eng
  • ISBN-13: 9789814740463
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The book constitutes an elementary course on Plane Euclidean Geometry, pitched at pre-university or at advanced high school level. It is a concise book treating the subject axiomatically, but since it is meant to be a first introduction to the subject, excessive rigour is avoided, making it appealing to a younger audience as well. The aim is to cover the basics of the subject, while keeping the subject lively by means of challenging and interesting exercises. This makes it relevant also for students participating in mathematics circles and in mathematics olympiads.Each section contains several problems, which are not purely drill exercises, but are intended to introduce a sense of "play" in mathematics, and inculcate appreciation of the elegance and beauty of geometric results. There is an abundance of colour pictures illustrating results and their proofs. A section on hints and a further section on detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study.
Preface vii
1 Geometric figures
1(28)
1.1 Points, lines, rays, line segments and length
1(4)
1.2 Angles and the degree measure
5(6)
1.3 The Parallel Postulate
11(3)
1.4 The Corresponding Angles Axiom
14(2)
1.5 Polygons
16(9)
1.6 Circles
25(4)
2 Congruent triangles
29(24)
2.1 SAS Congruency Rule
30(5)
2.2 SSS Congruency Rule
35(9)
2.3 ASA and AAS Congruency Rules
44(4)
2.4 SSA and RHS Congruency Rules
48(3)
2.5 Angle bisectors in a triangle are concurrent
51(2)
3 Quadrilaterals
53(28)
3.1 Characterizations of a parallelogram
54(7)
3.2 Areas
61(11)
3.3 Pythagoras's Theorem
72(9)
4 Similar triangles
81(24)
4.1 Basic Proportionality Theorem
83(3)
4.2 Criteria for similarity of triangles
86(14)
4.3 Areas of similar triangles
100(5)
5 Circles
105(58)
5.1 Area and circumference of a circle
109(5)
5.2 Circular arcs
114(31)
5.3 Tangent line to a circle
145(8)
5.4 An excursion in inversion
153(10)
Epilogue 163(4)
Hints 167(14)
Solutions 181(84)
Bibliography 265(2)
Index 267