Lectures on Euclidean Geometry. Volume 2: Circle measurement, Transformations, Space Geometry, Conics

✍ Scribed by Paris Pamfilos

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 456
• Category: Library

✦ Table of Contents

Preface
Symbol index
Contents
Part II Circle measurement, Transformations, Space Geometry, Conic sections
Chapter 1 Circle measurement
1.1 The difficulties, the limit
1.2 Definition of the perimeter of the circle
1.3 The number π
1.4 Arc length of a circle, radians
1.5 Definition of the area of the circle
1.6 The area of a circular sector
1.7 The isoperimetric inequality
1.8 Anthyphairesis
1.9 Comments and exercises for the chapter
References
Chapter 2 Transformations of the plane
2.1 Transformations, isometries
2.2 Reflections and point symmetries
2.3 Translations
2.4 Rotations
2.5 Congruency or isometry or equality
2.6 Homotheties
2.7 Similarities
2.8 Inversions
2.9 The hyperbolic plane
2.10 Archimedean tilings
2.11 Comments and exercises for the chapter
References
Chapter 3 Lines and planes in space
3.1 Axioms for space
3.2 Parallel planes
3.3 Angles in space
3.4 Skew lines
3.5 Line orthogonal to plane
3.6 Angle between line and plane
3.7 Theorem of Thales in space
3.8 Comments and exercises for the chapter
Chapter 4 Solids
4.1 Dihedral angles
4.2 Trihedral angles
4.3 Pyramids, polyhedral angles
4.4 Tetrahedra
4.5 Regular pyramids
4.6 Polyhedra, Platonic solids
4.7 Prisms
4.8 Cylinder
4.9 Cone, conical surface
4.10 Truncated cone, cone unfolding
4.11 Sphere
4.12 Spherical and circumscribed polyhedra
4.13 Spherical lune, angle of great circles
4.14 Spherical triangles
4.15 The supplementary trihedral
4.16 Axonometric projection, affinities
4.17 Perspective projection
4.18 Comments and exercises for the chapter
References
Chapter 5 Areas in space, volumes
5.1 Areas in space
5.2 Area of the sphere
5.3 Area of spherical polygons
5.4 Euler Characteristic
5.5 Volumes
5.6 Volume of prisms
5.7 Volume of pyramids
5.8 Volume of cylinders
5.9 Volume of cones
5.10 Volume of spheres
5.11 Comments and exercises for the chapter
References
Chapter 6 Conic sections
6.1 Conic sections
6.2 Dandelin’s spheres
6.3 Directrices
6.4 General characteristics of conics
6.5 The parabola
6.6 The ellipse
6.7 The hyperbola
6.8 Comments and exercises for the chapter
References
Chapter 7 Transformations in space
7.1 Isometries in space
7.2 Reflections in space
7.3 Translations in space
7.4 Rotations in space
7.5 Congruence or isometry in space
7.6 Homotheties in space
7.7 Similarities in space
7.8 Archimedean solids
7.9 Epilogue
References
Index