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E-grāmata: Geometry: A High School Course

4.12/5 (26 ratings by Goodreads)
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  • Formāts: PDF+DRM
  • Izdošanas datums: 17-Apr-2013
  • Izdevniecība: Springer-Verlag New York Inc.
  • Valoda: eng
  • ISBN-13: 9781475720228
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Geometry: A High School CoursePalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 17-Apr-2013
  • Izdevniecība: Springer-Verlag New York Inc.
  • Valoda: eng
  • ISBN-13: 9781475720228
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From the reviews: "A prominent research mathematician and a high school teacher have combined their efforts in order to produce a high school geometry course. The result is a challenging, vividly written volume which offers a broader treatment than the traditional Euclidean one, but which preserves its pedagogical virtues. The material included has been judiciously selected: some traditional items have been omitted, while emphasis has been laid on topics which relate the geometry course to the mathematics that precedes and follows. The exposition is clear and precise, while avoiding pedantry. There are many exercises, quite a number of them not routine. The exposition falls into twelve chapters: 1. Distance and Angles.- 2. Coordinates.- 3. Area and the Pythagoras Theorem.- 4. The Distance Formula.- 5. Some Applications of Right Triangles.- 6. Polygons.- 7. Congruent Triangles.- 8. Dilatations and Similarities.- 9. Volumes.- 10. Vectors and Dot Product.- 11. Transformations.- 12. Isometries.This excellent text, presenting elementary geometry in a manner fully corresponding to the requirements of modern mathematics, will certainly obtain well-merited popularity. Publicationes Mathematicae Debrecen#1

Papildus informācija

Springer Book Archives
Introduction ix
Chapter 1 Distance and Angles I
§1 Lines
1(7)
§2 Distance
8(5)
§3 Angles
13(16)
§4 Proofs
29(7)
§5 Right Angles and Perpendicularity
36(10)
§6 The Angles of a Triangle
46(16)
§7 An Application: Angles of Reflection
62(3)
Chapter 2 Coordinates
65(16)
§1 Coordinate Systems
65(6)
§2 Distance Between Points on a Line
71(2)
§3 Equation of a Line
73(8)
Chapter 3 Area and the Pythagoras Theorem
81(29)
§1 The Area of a Triangle
81(14)
§2 The Pythagoras Theorem
95(15)
Chapter 4 The Distance Formula
110(13)
§1 Distance Between Arbitrary Points
110(4)
§2 Higher Dimensional Space
114(5)
§3 Equation of a Circle
119(4)
Chapter 5 Some Applications of Right Triangles
123(39)
§1 Perpendicular Bisector
124(12)
§2 Isosceles and Equilateral Triangles
136(12)
§3 Theorems About Circles
148(14)
Chapter 6 Polygons
162(15)
§1 Basic Ideas
162(3)
§2 Convexity and Angles
165(4)
§3 Regular Polygons
169(8)
Chapter 7 Congruent Triangles
177(33)
§1 Euclid's Tests for Congruence
177(15)
§2 Some Applications of Congruent Triangles
192(8)
§3 Special Triangles
200(10)
Chapter 8 Dilations and Similarities
210(51)
§1 Definition
210(8)
§2 Change of Area Under Dilation
218(14)
§3 Change of Length Under Dilation
232(3)
§4 The Circumference of a Circle
235(10)
§5 Similar Triangles
245(16)
Chapter 9 Volumes
261(34)
§1 Boxes and Cylinders
261(9)
§2 Change of Volume Under Dilations
270(4)
§3 Cones and Pyramids
274(7)
§4 The Volume of the Ball
281(9)
§5 The Area of the Sphere
290(5)
Chapter 10 Vectors and Dot Product
295(26)
§1 Vector Addition
296(5)
§2 The Scalar Product
301(3)
§3 Perpendicularity
304(5)
§4 Projections
309(3)
§5 Ordinary Equation for a Line
312(4)
§6 The 3-Dimensional Case
316(3)
§7 Equation for a Plane in 3-Space
319(2)
Chapter 11 Transformations
321(35)
§1 Introduction
321(3)
§2 Symmetry and Reflections
324(7)
§3 Terminology
331(1)
§4 Reflection Through a Line
332(5)
§5 Reflection Through a Point
337(3)
§6 Rotations
340(6)
§7 Translations
346(2)
§8 Translations and Coordinates
348(8)
Chapter 12 Isometrles
356(35)
§1 Definitions and Basic Properties
356(7)
§2 Relations with Coordinates
363(4)
§3 Composition of Isometries
367(10)
§4 Definition of Congruence
377(4)
§5 Proofs of Euclid's Tests for Congruent Triangles
381(3)
§6 Isometries as Compositions of Reflections
384(7)
Index 391
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