Unsolved Problems in Geometry: Unsolved Problems in Intuitive Mathematics (Paperback, Softcover Repri)

'Notation and Definitions.- Sets. 1 Geometrical transformations..- Length, Area, and volume..- A. Convexity.- Al. The equichordal point problem..- A2. Hammer's 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. Dido's problem..- A21. Blaschke's problem..- A22. Minimal bodies of constant width..- A23. Constrained is operimetric problems..- A24. Is a body Fairly round if all its sections are?.- A25. How far apart can various centers be?.- A26. Dividing up a piece of land by a short fence..- A27. Midpoints of diameters of sets of constant width..- A28. Largest convex hull of an arc of a given length..- A29. Roads on planets..- A30. The shortest curve cutting all the lines through a disk..- A31. Cones based on convex sets..- A32. Generalized ellipses..- A33. Conic sections through five points..- A34. The shape of worn stones..- A35. Geodesics..- A36. Convex sets with universal sections..- A37. Convex space-filling curves..- A38. m-convex sets..- B. Polygons, Polyhedra, and Polytopes.- Bl. Fitting one triangle inside another..- B2. Inscribing polygons in curves..- B3. Maximal regular polyhedra inscribed in regular polyhedra..- B4. Prince Rupert's problem..- B5. Random polygons and polyhedra..- B6. Extremal problems for polygons..- B7. Longest chords of polygons..- B8. Isoperimetric inequalities for polyhedra..- B9. Inequalities for sums of edge lengths of polyhedra..- B10. Shadows of polyhedra..- B11. Dihedral angles of polyhedra..- B12. Monostatic polyhedra..- B13. Rigidity of polyhedra..- B14. Rigidity of frameworks..- B15. Counting polyhedra..- B16. The sizes of the faces of a polyhedron..- B17. Unimodality of f-vectors of polytopes..- B18. Inscribable and circumscribable polyhedra..- B19. Truncating polyhedra..- B20. Lengths of paths on polyhedra..- B21. Nets of polyhedra..- B22. Polyhedra with congruent faces..- B23. Ordering the faces of a polyhedron..- B24. The four color conjecture for toroidal polyhedra..- B25. Sequences of polygons and polyhedra..- C. Tiling and Dissection.- Cl. Conway's fried potato problem..- C2. Squaring the square..- C3. Mrs. Perkins's quilt..- C4. Decomposing a square or a cube into n smaller ones..- C5. Tiling with incomparable rectangles and cuboids..- C6. Cutting up squares, circles, and polygons..- C7. Dissecting a polygon into nearly equilateral triangles..- C8. Dissecting the sphere into small congruent pieces..- C9. The simplexity of the d-cube..- C10. Tiling the plane with squares..- C11. Tiling the plane with triangles..- C12. Rotational symmetries of tiles..- C13. Tilings with a constant number of neighbors..- C14. Which polygons tile the plane?.- C15. Isoperimetric problems for tilings..- C16. Polyominoes..- C17. Reptiles..- C18. Aperiodic tilings..- C19. Decomposing a sphere into circular arcs..- C20. Problems in equidecomposability..- D. Packing and Covering.- D1. Packing circles, or spreading points, in a square..- D2. Spreading points in a circle..- D3. Covering a circle with equal disks..- D4. Packing equal squares in a square..- D5. Packing unequal rectangles and squares in a square..- D6. The Rados' problem on selecting disjoint squares..- D7.