Geometric Probability on the Sphere
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Aigner, M., Ziegler, G.M.: Proofs from the Book. Springer, Berlin (1993). Reprint
Ambartzumyan, R.V., Mecke, J., Stoyan, D.: Geometrische Wahrscheinlichkeiten und stochastische Geometrie. Akademie-Verlag, Berlin (1993)
Artin, E.: The Gamma Function. Holt, Rinehart and Winston, New York (1964). Translated by M. Butler
Berger, M.: Geometry I and II. Springer, Berlin (1980)
Bigalke, H.-G.: Kugelgeometrie. Otto Salle Verlag, Frankfurt am Main (1984)
Bonnesen, T., Fenchel, W.: Theory of Convex Bodies. BCS Associates, Moscow (1987). Translated from the German edition from 1934
Brummelen, G.V.: Heavenly Mathematics—the Forgotten Art of Spherical Trigonometry. Princeton University Press, Princeton (2013)
Burago, Yu.D., Zalgaller, V.A.: Geometric Inequalities. Grundlehren Math. Wiss., vol. 285. Springer, Berlin (1988). Translated from the Russian
Cai, T., Fan, J., Jiang, T.: Distribution of angles in random packing on spheres. J. Mach. Learn. Res. 14, 1837–1864 (2013)
Chiu, S.K., Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic Geometry and Its Applications, 3rd edn. J. Wiley & Sons, Chichester (2013)
Feeman, T.G.: Portraits of the Earth. A Mathematician Looks at Maps. Mathematical World, vol. 18. American Mathematical Society, Providence (2002)
Frankl, P., Maehara, H.: Some geometric applications of the beta distribution. Ann. Inst. Stat. Math. 42, 463–474 (1990)
Gardner, R.J.: Geometric Tomography, 2nd edn. Encyclopedia of Mathematics and Its Applications, vol. 58. Cambridge University Press, New York (2006)
Giering, O.: Über gewisse Kennzeichnungen der Kugel. Math.-Phys. Semesterber. 18, 194–204 (1971)
Groemer, H.: Geometric Applications of Fourier Series and Spherical Harmonics. Encyclopedia of Mathematics and Its Applications, vol. 61. Cambridge University Press, Cambridge (1996)
Hoel, P.G., Port, S.C., Stone, C.J.: Introduction to Probability Theory. Houghton Mifflin Company, Boston (1971)
Hykšová, M.: Geometric probability applications through historical excursion. In: History and Epistemology in Mathematics Education, pp. 211–222. Vienna University of Technology, Vienna (2011)
Hykšová, M., Kalousová, A., Saxl, I.: Early history of geometric probability and stereology. Image Anal. Stereol. 31(1), 1–16 (2012)
Kendall, W.S., Molchanov, I. (eds.): New Perspectives in Stochastic Geometry. Oxford Univ. Press, Oxford (2010)
Kendall, M.G., Moran, P.A.P.: Geometric Probability. Charles Griffin and Company, London (1963)
Klain, D.A., Rota, G.C.: Introduction to Geometric Probability. Cambridge University Press, Cambridge (1997)
Laugwitz, D.: Differential and Riemannian Geometry. Academic Press, New York/London (1965)
Maeda, Y., Maehara, H.: Observing an angle from various viewpoints. In: Proc. JCDCG 2002. Lecture Notes Comp. Sci., vol. 2866, pp. 200–203 (2003)
Maehara, H.: On Sylvester’s problem. Proc. Inst. Stat. Math., Tokyo 25, 81–86 (1978). (In Japanese)
Maehara, H.: A threshold for the size of random caps to cover a sphere. Ann. Inst. Stat. Math. 40, 665–670 (1988)
Maehara, H.: On a condition for the union of spherical caps to be connected. J. Comb. Theory, Ser. A 101/102, 264–270 (2003)
Maehara, H.: When does the union of spherical caps become connected? Ann. Inst. Stat. Math. 56, 397–402 (2004)
Mathai, A.M.: An Introduction to Geometrical Probability. Gordon & Breach, Newark (1999)
Melzak, Z.A.: Invitation to Geometry. John Wiley & Sons Inc., New York (1983)
Miles, R.E.: On random rotations in R 3 $R^{3}$ . Biometrika 52, 636–639 (1965)
Miles, R.E.: Random points, sets and tessellations on the surface of a sphere. Sankya A 33, 145–174 (1971)
Mood, A.M., Graybill, F.A., Boes, D.C.: Introduction to the Theory of Statistics, 3rd edn. McGraw-Hill Series in Probability and Statistics. McGraw-Hill Book Company, New York (1974)
Moran, P.A.P.: An Introduction to Probability Theory. Clarendon Press, Oxford (1968)
Penrose, M.D., Wade, A.R.: Multivariate normal approximation in geometric probability. J. Stat. Theory Pract. 2, 293–326 (2008)
Penrose, M.D., Yukich, J.E.: Normal approximation in geometric probability. In: Barbour, A.D., Chen, L.H.Y. (eds.) Stein’s Method and Applications, pp. 37–58. World Scientific, Singapore (2005)
Rényi, A.: On a one-dimensional problem concerning random place filling. Magy. Tud. Akad. Mat. Kut. Intéz. Közl. 3, 109–127 (1958). (In Hungarian)
Santaló, L.A.: Integral formulas in Crofton’s style on the sphere and some inequalities referring to spherical curves. Duke Math. J. 9, 707–722 (1942)
Santaló, L.A.: Integral Geometry and Geometric Probability. Encyclopedia of Mathematics and Its Applications, vol. 1. Addison-Wesley, London (1976)
Schmidt, V. (ed.): Stochastic Geometry, Spatial Statistics and Random Fields. Models and Algorithms. Lecture Notes Math., vol. 2120. Springer, Berlin (2015)
Schneider, R., Weil, W.: Stochastic and Integral Geometry. Probability and Its Applications, vol. 151. Cambridge University Press, Cambridge (2008)
Seneta, E., Parshall, K.H., Jongmans, F.: Nineteenth century developments in geometric probability: J.J. Sylvester, M.W. Crofton, J.-É. Barbier, and J. Bertrand. Arch. Hist. Exact Sci. 55, 501–524 (2001)
Solomon, H.: Geometric Probability. Society for Industrial and Applied Mathematics, Philadelphia (1978)
Watson, S.: Random points on hyperplanes. In: Stochastic Geometry, Geometric Statistics and Stereology, Oberwolfach, Teubner-Texte. Wiley, New York (1983)
Weil, W., Wieacker, J.A.: Stochastic geometry. In: Handbook of Convex Geometry, Vol. A, B, pp. 1391–1438. North-Holland, Amsterdam (1993)