## Unsolved Problems in Geometry: Unsolved Problems in Intuitive MathematicsMathematicians 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. |

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### Contents

Geometrical transformations 3 Length area and volume | 4 |

B Polygons Polyhedra and Polytopes | 48 |

Tiling and Dissection | 79 |

Packing and Covering | 107 |

E Combinatorial Geometry | 131 |

F Finite Sets of Points | 149 |

G General Geometric Problems | 168 |

sets of a given area 182 G14 Sets containing large triangles | 182 |

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### Common terms and phrases

3-dimensional Amer analogs asked ball Borsuk's conjecture boundary bounded Bull C. A. Rogers Cambridge Philos Canad centro-symmetric Chakerian chord combinatorial geometry configurations congruent copies conjecture constant width contains convex body convex hull convex polygon convex polyhedra convex sets Croft cube curve Danzer diameter dimensions Discrete Math disk dissection distance edges Elem equidecomposable equilateral triangle Erdös Euclidean Euclidean space example faces Fejes Tóth Figure finite Geom given graphs Grünbaum Hadwiger Helly's theorem hexagon Hungar inequalities integer intersection isoperimetric Klee Larman lattice points least Lebesgue measure length London Math Mathematical maximum minimal minimum Minkowski's theorem Monthly Moser n-gon Pach packing perimeter plane convex set plane set polyhedra polyhedron polyominoes polytopes possible problem Proc radius rectangle regular Reuleaux triangle Section set of points Shephard showed simplex smallest sphere spherical square Steinhaus subset surface area symmetric tetrahedron theorem Theory tile the plane unit vertex vertices volume W. T. Tutte