Unsolved Problems in Geometry Unsolved Problems in Intuitive Mathematics [Hardcover]

Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from amateurs to research mathematicians.Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from amateurs to research mathematicians.Notation and Definitions.- Sets. 1 Geometrical transformations..- Length, Area, and volume..- A. Convexity.- Al. The equichordal point problem..- A2. Hammers x-ray problems..- A3. Concurrent normals..- A4. Billiard ball trajectories in convex regions..- A5. Illumination problems..- A6. The floating body problem..- A7. Division of convex bodies by lines or planes through a point..- A8. Sections through the centroid of a convex body..- A9. Sections of centro-symmetric convex bodies..- A10. What can you tell about a convex body from its shadows?.- A11. What can you tell About a convex body from its sections?.- A12. Overlapping convex bodies..- A13. Intersections of congruent surfaces..- A14. Rotating polyhedra..- A15. Inscribed and circumscribed centro-symmetric bodies..- A16. Inscribed affine copies of convex bodies..- A17. Isoperimetric inequalities and extremal problems..- A18. Volume against width..- A19. Extremal problems for elongated sets..- A20. Didos problem..- A21. Blaschkes problem..- A22. Minimal bodil#