Abstract
The study of mathematical practice is not the private property of philosophers. Many other disciplines, especially including mathematicians, are engaged in it. As a case study, an elementary derivation of Heon’s area formula is presented, and then analyzed methodologically and ontologically.
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References
Albers, Donald J., and Gerald L. Alexanderson. 1985 “Mathematical People”. Birkhauser, Boston, 1985.
Albers, Donald J. , Gerald L. Alexanderson and Constance Reid. 1990. “More Mathematical People.” Birkhauser, Boston 1990.
Alperin, C. “Heron’s Area Formula,” The College Mathematics Journal, March 1987, v. 18, no.2, pp. 137-8.
Arnold.V. I. “Huygens and Barrow, Newton and Hooke.” Birkhauser, Boston, 1990.
Arnold, V. et al., editors. “Mathematics: Frontiers and Perspectives.” International Mathematical Union and American Mathematicsl Society, 2000.
Crowe, M. “Ten “laws” Concerning Patterns of Change in the History of Mathematics. Historia Mathematica, 2, 161-166 (1975)
Davis, P.J. “Fidelity in Mathematical Discourse: Is 1+1 Really 2?” American Mathematical Monthly 78, 252-263 (1972)
Dehaene, Stanislas. “The Number Sense”. Oxford University Press, New York, 1997.
Dieudonné, J. “The Work of Nicholas Bourbaki.” American Mathematical Monthly. 77, 134-145 (1970)
Dorrie, Heinrich. “100 Great Problems of Elementary Mathematics,” Dover Publications, New York, 1965.
Dunham, William. “Journey through Genius,” Penguin Books, New York, 1990.
Hadamard, J. “The Psychology of Invention in the Mathematical Field.” Dover Publications, New York, 1945.
Halmos, P. “Mathematics as a Creative Art.” American Scientist. 56, 375-389 (1968)
Hardy, G. H. “Mathematical Proof.” Mind. 38, 1-25 (1929)
Hersh, R. “What is Mathematics, Really?” Oxford University Press, New York, 1997.
Hersh, R. November 2002, “A Nifty Derivation of Heron’s Area Formula by 11th Grade Algebra.” Focus, v. 22, no.8, p. 22
Kac, M. 1985, “Enigmas of Chance” Harper and Row, New York.
Kitcher, P. “The Nature of Mathematical Knowledge.” Oxford University Press, 1983.
Lakatos, I. “Proofs and Refutations.” Cambridge University Pres, 1976.
Lévy, P. “Quelques Aspects de la Pensée d’un Mathematicien.” Albert Blanchard 1970.
Littlewood, J. E. “Littlewood’s Miscellany.” Cambridge University Press, 1986.
MacLane, S. “Mathematics: Form and Function”: New York. Springer-Verlag, 1986.
Mozzochi, . J. “The Fermat Diary.” American Mathematical Society, 2000.
Peirce, C. S. “The Essence of Mathematics,” “Essays in the Philosophy of Science”, Indianapolis: Bobbs-Merrill, 1957.
Pier, Jean-Paul, editor. “Development of Mathematics, 1950-2000.” Birkhauser Boston, 2000.
Poincaré, Henri. “Mathematical Creation” “The Foundations of Science”. The Science Press, New York, 1913.
Poincaré, Henri. “The Nature of Mathematical Reasoning.” “Science and Hypothesis.” Dover Publications, New York, 1952.
Polya, G. “How to Solve It.” Princeton University Pres, 1971.
Polya, G. “Mathematical Discovery.” John Wiley & Sons, 1971.
Polya, G. “Mathematics and Plausible Reasoning.” Princeton University Press, 1954.
Reid, C. “Hlbert.” Springer, 1972.
Reid, C. “Courant in Gottingen and New York.” Springer, 1976.
Rényi, A. “Dialogues on Mathematics.” San Francisco: Holden-Day, 1967.
Rota, Gian-Carlo. “Indiscrete Thoughts.” Birkhauser, Boston, 1997.
Schwartz, L. “A Mathematician Grappling With His Century.” Birkhauser, 2001.
Ulam, S. “Adventures of a Mathematician.” Charles Scribner’s Sons, 1983.
Von Neumann, J. 1947, “The Mathematician” Robert B. Heywood (ed.) “Works of the Mind,” Chicago, University of Chicago Press.
Wiener, Norbert. “Ex-Prodigy.” M.I.T. Press. 1964.
Wiener, Norbert. “I am a Mathematician.” M.I.T. Press, 1956.
Wilder, Raymond L. “The Evolution of Mathematical Concepts.” New York, John Wiley & Sons. 1968.
Wilder, Raymond L. “Hereditary Stress as a Cultural Force in Mathematics.” Historia Mathematica, 1, 29-46 (1974)
Wilder, Raymond L. “Mathematics as a Cultural System,” New York. Pergamon, 1981.
Yandell, Benjamin H. “The Master Class.” A.K. Peters, 2002.
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Hersh, R. (2007). On The Interdisciplinary Study of Mathematical Practice, with a Real Live Case Study. In: van Kerkhove, B., van Bendegem, J.P. (eds) Perspectives On Mathematical Practices. Logic, Epistemology, and the Unity of Science, vol 5. Springer, Dordrecht. https://doi.org/10.1007/1-4020-5034-8_13
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DOI: https://doi.org/10.1007/1-4020-5034-8_13
Publisher Name: Springer, Dordrecht
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