Bibliography for Monte Carlo Pi

unabridged

 

  1. A mixture representation of pi with applications in Markov chain Monte Carlo and perfect sampling PDF   
    Hobert, James P.; Robert, Christian P.
    Ann. Appl. Probab.  14  (2004),  no. 3, 1295--1305, MathSciNet.  
  2. Buffon's Needle on Caustics and Torus Quantization
    Lavenda B.H.
    Open Systems and Information Dynamics, 2003, vol. 10, no. 1, pp. 51-64(14), Ingenta.   
  3. The Buffon's needle problem and the design of a geophysical survey
    Sambuelli, Luigi ; Strobbia, Claudio
    Geophysical Prospecting, v 50, n 4, July, 2002, p 403-409, Compendex.
  4. How likely is Buffon's needle to fall near a planar Cantor set?  
    Peres, Yuval; Solomyak, Boris
    Pacific J. Math.  204  (2002),  no. 2, 473--496, MathSciNet.  
  5. The accuracy of Buffon's needle: a rule of thumb used by ants to estimate area
    S.T. Mugford; E.B. Mallon; N.R. Franks
    Behavioral Ecology, November 2001, vol. 12, no. 6, pp. 655-658(4), Ingenta.    
  6. Ants estimate area using Buffon's needle
    Mallon E. B.; Franks N. R.
    Proceedings: Biological Sciences, 22 April 2000, vol. 267, no. 1445, pp. 765-770(6), Ingenta.     
  7. On a problem of Buffon type for triangular lattices and a "non-small" needle.
    Pettineo, Maria
    III International Conference in "Stochastic Geometry, Convex Bodies and Empirical Measures", Part I (Mazara del Vallo, 1999).  Rend. Circ. Mat. Palermo (2) Suppl.  No. 65, part I (2000), 247--255, MathSciNet.  
  8. Buffon's short needle on the sphere.  
    Isokawa, Yukinao
    Bull. Fac. Ed. Kagoshima Univ. Natur. Sci.  51  (1999), 17--36 (2000), MathSciNet.  
  9. Problems of Buffon type for "non-small" needles.  
    Duma, Andrei
    Rend. Circ. Mat. Palermo (2)  48  (1999),  no. 1, 23--40, MathSciNet.  
  10. Buffon got it straight
    Wood G.R.; Robertson J.M.
    Statistics and Probability Letters, 30 March 1998, vol. 37, no. 4, pp. 415-421(7), Ingenta.      
  11. Information in Buffon experiments
    Robertson J.M.; Wood G.R.
    Journal of Statistical Planning and Inference, 5 January 1998, vol. 66, no. 1, pp. 21-37(17), Ingenta.      
  12. Convex bodies instead of needles in Buffon's experiment.  
    Aleman, A.; Stoka, M.; Zamfirescu, T.
    Geom. Dedicata  67  (1997),  no. 3, 301--308, MathSciNet.  
  13. On Laplace's Extension of the Buffon Needle Problem (in Classroom Capsules)  
    Barry J. Arnow  
    The College Mathematics Journal, Vol. 25, No. 1. (Jan., 1994), pp. 40-43, Jstor.  
  14. Buffon Noodles  
    Ed Waymire  
    The American Mathematical Monthly, Vol. 101, No. 6. (Jun. - Jul., 1994), pp. 550-559, Jstor.  
  15. Determining Sample Sizes for Monte Carlo Integration (in Classroom Computer Capsules)  
    David Neal  
    The College Mathematics Journal, Vol. 24, No. 3. (May, 1993), pp. 254-259, Jstor.  
  16. A Monte Carlo Application to Approximate [Graphics:../Images/MonteCarloPiBib_gr_2.gif]   
    Kenneth Easterday and Tommy Smith   
    School Science and Mathematics, Vol. 92, No. 1, (1992), pp. 23-25.   
  17. Buffon's Needle Problem on Radial Lines (in Notes)  
    H. J. Khamis  
    Mathematics Magazine, Vol. 64, No. 1. (Feb., 1991), pp. 56-58, Jstor.  
  18. A Monte Carlo Application to Approximate Pi.
    Easterday, Kenneth; Smith, Tommy
    Mathematics Teacher v84 n5 p387-90 May 1991, ERIC.  
  19. Rudolf Wolf's Contribution to the Buffon Needle Problem (an Early Monte Carlo Experiment) and Application of Least Squares  
    Hans Riedwyl  
    The American Statistician, Vol. 44, No. 2. (May, 1990), pp. 138-139, Jstor.  
  20. Experimental Pi.
    Corris, G.
    Mathematics in School v19 n1 p18-21 Jan 1990, ERIC.  
  21. The problem of casting the Buffon needle in the plane and its generalization. (Chinese)  
    Huang, Jian An
    Hunan Jiaoyu Xueyuan Xuebao (Ziran Kexue)  7  (1989),  no. 2, 67--72, MathSciNet.  
  22. Some extensions of the Buffon needle problem. (Chinese)  
    Guo, Ziying
    Qufu Shifan Daxue Xuebao Ziran Kexue Ban  14  (1988),  no. 3, 154--158, MathSciNet.  
  23. Designing Buffon's Needle for a Given Crossing Distribution  
    Jack M. Robertson; Andrew F. Siegel  
    The American Mathematical Monthly, Vol. 93, No. 2. (Feb., 1986), pp. 116-119, Jstor.  
  24. Generalized Buffon's needle problem and some remarks on its application. (Japanese)  
    Taga, Yasushi
    Proc. Inst. Statist. Math.  34  (1986),  no. 1, 29--37, MathSciNet.  
  25. Sur quelques problèmes de probabilités du type aiguille de Buffon. (French) [Some probability problems of the Buffon needle type]  
    Altomare, Francesco
    Publ. Inst. Statist. Univ. Paris  30  (1985),  no. 1-2, 1--14, MathSciNet.  
  26. A remark on Buffon's needle problem.  
    Abel, Ulrich
    Elem. Math.  39  (1984),  no. 2, 34--37.
  27. Buffon Needle Method of Track Counting  
    Gold, R.; Roberts, J. H.; Ruddy, F. H.
    Pergamon Press, 1982, p 891-897, Compendex.  
  28. Zur Simulation des Buffon-Nadelproblems. (German) [On the simulation of Buffon's needle problem]  
    Bentz, Hans-J.
    Praxis Math.  24  (1982), no. 5, 129--137, MathSciNet.  
  29. A variant of the problem of Buffon's needle. (Italian)  
    Girone, G.
    Atti Accad. Sci. Lett. Arti Palermo Parte I (4)  39  (1979/80), 221--229 (1982), MathSciNet.  
  30. An Irrational Calculation of Pi.
    Lowry, Pat G.
    Creative Computing v7 n12 p238-39 Dec 1981, ERIC.  
  31. Monte Carlo, Probability, Algebra, and Pi.
    Hinders, Duane C.
    Mathematics Teacher v74 n5 p335-39 May 1981, ERIC.  
  32. Application of the Buffon needle problem and its extensions to parallel-line search sampling scheme.  
    Chung, C. F.
    J. Internat. Assoc. Math. Geol.  13  (1981), no. 5, 371--390, MathSciNet.  
  33. Constructing Buffon Curves from their Distributions  
    Duane W. DeTemple; Jack M. Robertson  
    The American Mathematical Monthly, Vol. 87, No. 10. (Dec., 1980), pp. 779-784, Jstor.  
  34. Larval Fish, Power Plants, and Buffon's Needle Problem  
    Sherwood F. Ebey; John J. Beauchamp  
    The American Mathematical Monthly, Vol. 84, No. 7. (Aug. - Sep., 1977), pp. 534-541, Jstor.  
  35. Buffon's problem with a long needle.  
    Diaconis, Persi
    J. Appl. Probability  13  (1976), no. 3, 614--618, MathSciNet.  
  36. A Precalculus Unit on Area under Curves (in Computer Corner)  
    Samuel Goldberg
    The Two-Year College Mathematics Journal, Vol. 6, No. 4. (Dec., 1975), pp. 29-35, Jstor.  
  37. Sharpening Buffon's Needle  
    Michael D. Perlman; Michael J. Wichura  
    The American Statistician, Vol. 29, No. 4. (Nov., 1975), pp. 157-163, Jstor.  
  38. Buffon's Needle Experiment  
    E. F. Schuster  
    The American Mathematical Monthly, Vol. 81, No. 1. (Jan., 1974), pp. 26-29, Jstor.  
  39. Monte Carlo Estimate for Pi  
    John H. Mathews  
    Pi Mu Epsilon Journal, Vol. 5, 1972, pp. 281-282.
  40. Buffon in the Round  
    M. F. Neuts; P. Purdue  
    Mathematics Magazine, Vol. 44, No. 2. (Mar., 1971), pp. 81-89, Jstor.  
  41. Buffon's Noodle Problem (in Mathematical Notes)  
    J. F. Ramaley  
    The American Mathematical Monthly, Vol. 76, No. 8. (Oct., 1969), pp. 916-918, Jstor.  
  42. Some extensions of Buffon's "needle problem". (Romanian)  
    Trandafir, Rodica
    Stud. Cerc. Mat.  21  1969 799--803, MathSciNet.  
  43. A Variation of the Buffon Needle Problem  
    R. L. Duncan  
    Mathematics Magazine, Vol. 40, No. 1. (Jan., 1967), pp. 36-38, Jstor.  
  44. The Monte Carlo Method   
    Y. A. Shreider  
    Pergamon Press, 1966
  45. On Barbier's Solution of the Buffon Needle Problem  
    Murray S. Klamkin  
    Mathematics Magazine, Vol. 28, No. 3. (Jan. - Feb., 1955), pp. 135-138, Jstor.  
  46. The Monte Carlo Method  
    D. D. McCracken  
    Scientific American, 192, (May 1955), pp. 90-96.  
  47. An Extension of the Buffon Needle Problem (in Notes)  
    Nathan Mantel  
    The Annals of Mathematical Statistics, Vol. 24, No. 4. (Dec., 1953), pp. 674-677, Jstor.  
  48. On the Uniqueness of the Distribution Function for the Buffon Needle Problem  
    M. S. Klamkin  
    The American Mathematical Monthly, Vol. 60, No. 10. (Dec., 1953), pp. 677-680, Jstor.  
  49. An extension of the Buffon needle problem.  
    Mantel, Nathan
    Ann. Math. Statistics  24,  (1953). 674--677, MathSciNet.  
  50. On Buffon's Problem and Its Generalizations  
    M. Kac; E. R. van Kampen; Aurel Wintner  
    American Journal of Mathematics, Vol. 61, No. 3. (Jul., 1939), pp. 672-676, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005