References
BagemihlF., ‘A conjecture concerning neighboring tetrahedra’, Am. Math. Monthly 63 (1956) 328–329.
BastonV. J. D., Some Properties of Polyhedra in Euclidean Space, Pergamon Press, Oxford, England, 1965.
BlumenthalL. M., Theory and Applications of Distance Geometry, Clarendon Press, Oxford, England, 1953.
CoxeterH. S. M., ‘A problem of collinear points’, Am. Math. Monthly 55 (1948) 26–28.
CoxeterH. S. M., Introduction to Geometry, Wiley, New York, N.Y., 1961.
CoxeterH. S. M., ‘The problem of packing a number of equal nonoverlapping circles on a sphere’, Trans. N.Y. Acad. Sci. (2) 24 (1962), 320–331.
CroweD. W. and T. A.McKee, ‘Sylvester's problem on collinear points’, Math. Magazine 41 (1968), 30–34.
DiracG. A., ‘Collinearity properties of sets of points’, Quart. J. Math. (Oxford Series) 2 (1951), 221–227.
FreeseR. W., A. K.Miller, and Z.Usiskin, ‘Can every triangle be divided into n triangles similar to it?’, Am. Math. Monthly 77 (1970), 867–869.
Grünbaum, B., ‘The importance of being straight’, in Proceedings of the Twelfth Biennial Seminar (Time Series and Stochastic Processes; Convexity and Combinatorics), Canadian Mathematical Congress, Montreal, Canada, 1970, 243–254.
HadwigerH., ‘Ungelöste Probleme, Nr. 40’, Elemente Math. 16 (1961), 103–104.
KellyL. M., ‘Covering problems’, Math. Magazine 19 (1944–45), 123–130.
KellyL. M. and W. O. J.Moser, ‘On the number of ordinary lines determined by n points’, Can. J. Math. 10 (1958), 210–219.
KleeV., ‘Can nine tetrahedra form a neighboring family?’, Am. Math. Monthly 76 (1969), 178–179.
KleeV., ‘Is every polygonal plane region illuminable from some point?’, Am. Math. Monthly 76 (1969), 180.
Klee, V., Shapes of the Future, I and II. Two films produced by the Educational Development Center, Newton, Mass., for the Individual Lecture Film Project of the Mathematical Association of America, 1970 and 1971. Available from Modern Learning Aids, P.O. Box 302, Rochester, N.Y.
MeschkowskiH., Unsolved and Unsolvable Problems in Geometry (trans. from German by J. A. C. Burlak), F. Ungar, New York, N.Y., 1966.
MonskyP., ‘On dividing a square into triangles’, Am. Math. Monthly 77 (1970), 161–164.
Penrose, L. S. and R. Penrose, ‘Puzzles for Christmas’, The New Scientist 25 December 1958, 1580–1581, 1597.
RobinsonR. M., ‘Finite sets of points on a sphere with each nearest to five others’, Math. Ann. 179 (1969), 296–318.
SylvesterJ. J., ‘Mathematical Question 11851’, Educational Times 59 (1893), 98.
ThomasJ., ‘A dissection problem’, Math. Magazine 41 (1968), 187–190.
TietzeH., Famous Problems of Mathematics, Graylock Press, Baltimore, Md., 1965.
Usiskin, Z. and S. G. Wayment, ‘Partitioning a triangle into 5 triangles similar to it’, Math. Magazine 44 (1971), to appear.
Van derWaerdenB. L., ‘Pollenkörner, Punktverteilungen auf der Kugel und Informationstheorie’, Naturwissenschaften 7 (1961), 189–192.
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Klee, V. The use of research problems in high school geometry. Educ Stud Math 3, 482–489 (1971). https://doi.org/10.1007/BF00302309
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DOI: https://doi.org/10.1007/BF00302309