The Problem of Points

Cantillo, Andres (2011): The Problem of Points.

Abstract

According to Katz [6] some of the basic notions of probability existed in ancient civilizations. In The Talmud and in Roman calculations of annuities there is some evidence of this. However, no record of numerical probability calculations exists. Hald [5], Bernstein [1] and Katz [6] agree that this numerical development was intimately linked to the study of gambling, contracts and profits. These authors also coincide in that the formulation of “The Problem of Points” is a crucial event. The paper is centered on evaluating and explaining the history of the formulation of “The Problem of Points”. The solution to this problem originated the deductive notions of probability [5]. I will center my attention on the formulation and attempt of solution by Pacioli [4], Cardano [2], Tartaglia [14] and Forestani [4]. In this process Cardano began to unveil some principles that are coherent with a modern theory of probability.

• Item Type: MPRA Paper
• Language: English
• Keywords: History of Probability; Uncertainty
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C19 - Other; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C79 - Other; Y - Miscellaneous Categories > Y8 - Related Disciplines > Y80 - Related Disciplines

References

1. Bernstein, P. (1996). Against the Gods. New York: John Wiley and Sons.

2. Cardano, G. (1539). Practica Arithmetice et mensurandi singularis. Milan.

3. Cardano, G. (1503). The Book on Games of Chance.

4. Forestani, L. (1602). Libro Quinto, pp. 364–367, Edition of 1682. In L. Forestani, Pratica D'arithmetica e Geometria (pp. 364-367). Venice.

5. Hald, A. (1990). A History of Probability and Statistics and Their Applications before 1750. New York: Wiley.

6. Katz, V. (2009). A History of Mathematics. Boston: Addison-Wesley.

7. Ore, O. (1953). The Gambling Scholar . Princeton: Princeton University Press.

8. Pacioli, L. (1494). Summa de Arithmetica Geometria Proportioni Et Proportionalita. Venice.

9. Pulskamp, R. (2009 a). Summa de Arithmetica, geometria e proportionalita. Retrieved Feb 9, 2011, from http://www.cs.xu.edu/math/Sources/Pacioli/summa.pdf

10. Pulskamp, R. (2009 b, July 18). Prima parte del General Tratatto Book 16, Section 206 . Retrieved February 28, 2011, from http://www.cs.xu.edu/math/Sources/Tartaglia/tartaglia_trattato_2col.pdf

11. Pulskamp, R. (2009 c, Februari 15). Practica D' Arithmetica E GEometria. Retrieved Februari 28, 2011, from http://www.cs.xu.edu/math/Sources/Forestani/forestani%20on%20points.pdf

12. Pulskamp, R. (2009 d, July 18). Practica arithmetice et mensurandi singularis. Retrieved February 2, 2011, from http://www.cs.xu.edu/math/Sources/Cardano/cardan_pratica.pdf

13. Tartaglia, N. (1556). General tratatto di numeri e misure. Venezia.

14. Tartaglia, N. (1556). La Prima Parte del General Tratatto Di Numeri, Et Misure . In Book 16, Section 206 . Venice.

15. Delaware, R. (2011). Class Notes Math 464, University of Missouri Kansas City, de Mere’s problem and Pascal’s solution.