General Geometric Problems

[1]  D. E. Raiskii Realization of all distances in a decomposition of the space Rn into n+1 parts , 1970 .

[2]  N. R. Wagner The Sofa Problem , 1976 .

[3]  H. Hadwiger Ueberdeckung des Euklidischen Raumes durch kongruente Mengen , 1945 .

[4]  J. A. D. Reyna Some results connected with a problem of Erdős. III , 1983 .

[5]  I. J. Schoenberg On the Besicovitch-Perron Solution of the Kakeya Problem , 1988 .

[6]  K. Binmore On Turan's Lemma , 1971 .

[7]  J. A. Haight A linear set of infinite measure with no two points having integral ratio , 1970 .

[8]  V. Rödl,et al.  All triangles are Ramsey , 1986 .

[9]  Metrically homogeneous sets , 1968 .

[10]  K. Falconer The Realization of small Distances in Plane Sets of Positive Measure , 1986 .

[11]  Ronald L. Graham,et al.  OLD AND NEW EUCLIDEAN RAMSEY THEOREMS , 1985 .

[12]  On the average distance property of compact connected metric spaces , 1983 .

[13]  D. G. Larman,et al.  A Problem of Incidence , 1968 .

[14]  O. Perron,et al.  Über einen Satz von Besicovitsch , 1928 .

[15]  K. Falconer Continuity properties of k-plane integrals and Besicovitch sets , 1980, Mathematical Proceedings of the Cambridge Philosophical Society.

[16]  J. M. Marstrand Packing smooth curves in Rq , 1979 .

[17]  Leslie E. Shader All Right Triangles Are Ramsey in E2 , 1976, J. Comb. Theory, Ser. A.

[18]  A property of compact connected spaces , 1981 .

[19]  P. Erdös Some combinatorial, geometric and set theoretic problems in measure theory , 1984 .

[20]  Nicholas C. Wormald,et al.  Bounds on the measurable chromatic number of Rn , 1989, Discret. Math..

[21]  Péter Komjáth Large Sets not Containing Images of a Given Sequence , 1983, Canadian Mathematical Bulletin.

[22]  F. A. Bostock,et al.  On a Theorem of Larman , 1972 .

[23]  Rozália Juhász Ramsey Type Theorems in the Plane , 1979, J. Comb. Theory, Ser. A.

[24]  The average distance property for subsets of euclidean space , 1988 .

[25]  F. Cunningham THE KAKEYA PROBLEM FOR SIMPLY CONNECTED AND FOR STAR-SHAPED SETS , 1971 .

[26]  Ronald L. Graham On Partitions of En , 1980, J. Comb. Theory, Ser. A.

[27]  Roy O. Davies,et al.  Some remarks on the Kakeya problem , 1971, Mathematical Proceedings of the Cambridge Philosophical Society.

[28]  R. Guy Monthly Research Problems, 1969–77 , 1977 .

[29]  V. Rödl,et al.  A partition property of simplices in Euclidean space , 1990 .

[30]  K. Falconer The geometry of fractal sets , 1985 .

[31]  H. E. Debrunner,et al.  Can you cover your shadows? , 1986, Discret. Comput. Geom..

[32]  Alan Horwitz Reconstructing a function from its set of tangent lines , 1989 .

[33]  Wacław Sierpiński,et al.  Cardinal and Ordinal Numbers , 1966 .

[34]  K. J. FALCONER,et al.  The Realization of Distances in Measurable Subsets Covering Rn , 1981, J. Comb. Theory, Ser. A.

[35]  K. Falconer The geometry of fractal sets: Contents , 1985 .

[36]  J. Spencer Ramsey Theory , 1990 .

[37]  Micha Sharir,et al.  An efficient motion-planning algorithm for a convex polygonal object in two-dimensional polygonal space , 1990, Discret. Comput. Geom..

[38]  H. T. Croft THREE LATTICE-POINT PROBLEMS OF STEINHAUS , 1982 .

[39]  Peter Frankl,et al.  Intersection theorems with geometric consequences , 1981, Comb..

[40]  V. Klee Some Unsolved Problems in Plane Geometry , 1979 .

[41]  H. Hadwiger,et al.  Ein ?berdeckungssätze für den Euklidischen Raum , 1944 .

[42]  László A. Székely,et al.  Measurable chromatic number of geometric graphs and sets without some distances in euclidean space , 1984, Comb..

[43]  L. Santaló Integral geometry and geometric probability , 1976 .

[44]  A. Besicovitch On Kakeya's problem and a similar one , 1928 .

[45]  D. G. Larman,et al.  Arcs with increasing chords , 1972 .

[46]  J. M. Marstrand Packing planes in ℝ 3 , 1979 .

[47]  D. G. Larman A note on the realization of distances within sets in euclidean space , 1978 .

[48]  K. Falconer,et al.  Plane Sets with Positive Density at Infinity Contain all Large Distances , 1986 .

[49]  An average distance result in Euclidean n-space , 1982, Bulletin of the Australian Mathematical Society.

[50]  Paul Erdös,et al.  Euclidean Ramsey Theorems I , 1973, J. Comb. Theory, Ser. A.

[51]  Gilbert Strang,et al.  The Width of a Chair , 1982 .

[52]  Paul Erdös COMBINATORIAL PROBLEMS IN GEOMETRY AND NUMBER THEORY , 1979 .

[53]  Leo Moser Moving Furniture Through a Hallway , 1966 .

[54]  Sidney A. Morris,et al.  NUMERICAL GEOMETRY-NUMBERS FOR SHAPES , 1986 .

[55]  W. Sierpinski Sur un problème de H. Steinhaus concernant les ensembles de points sur le plan , 1958 .

[56]  J. M. Marstrand On Khinchin's Conjecture about Strong Uniform Distribution , 1970 .

[57]  H. Steinhaus Length, shape and area , 1954 .

[58]  Construction of sets of positive measure not containing an affine image of a given infinite structure , 1987 .

[59]  C. Rogers,et al.  The realization of distances within sets in Euclidean space , 1972 .

[60]  Douglas R. Woodall Distances Realized by Sets Covering the Plane , 1973, J. Comb. Theory, Ser. A.

[61]  On maximal Euclidean sets avoiding certain distance configurations , 1981 .

[62]  Average distances in compact connected spaces , 1982, Bulletin of the Australian Mathematical Society.

[63]  K. J. Falconer On a problem of Erdős on sequences and measurable sets , 1984 .

[64]  Paul Erdös,et al.  Colouring the real line , 1985, J. Comb. Theory B.

[65]  J. Bourgain,et al.  A szemerédi type theorem for sets of positive density inRk , 1986 .