Invitation to Geometry

Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. Only a slight acquaintance with mathematics beyond the high-school level is necessary, including some familiarity with calculus and linear algebra.
This text's introductions to several branches of geometry feature topics and treatments based on memorability and relevance. The author emphasizes connections with calculus and simple mechanics, focusing on developing students' grasp of spatial relationships. Subjects include classical Euclidean material, polygonal and circle isoperimetry, conics and Pascal's theorem, geometrical optimization, geometry and trigonometry on a sphere, graphs, convexity, and elements of differential geometry of curves. Additional material may be conveniently introduced in several places, and each chapter concludes with exercises of varying degrees of difficulty.

1. Heron's Formula and Related Ones

2. Triangle Transversals

3. Rotation and Rolling

4. Oblique Sections of Certain Solids

5. Conic Sections of Certain Solids

6. Examples of Geometrical Extrema

7. Simple Geometry and Trigonometry on the Sphere

8. Introduction to Graphs

9. Elements of Convexity

10. Curves in Space and Curves on Surfaces

Notes

Bibliography

Index