Abstract
There are many possible ways of introducing the number π, associated with the circle. We shall obtain π from the complex exponential function
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And he made a molten sea, ten cubits from the one brim to the otherj it was round all about, and his height was five cubits, and a line of thirty cubits did compass it round about. (I Kings, Chapter 7, verse 23).
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Further Reading
Beckmann, Peter, A History of Pi. Boulder, Col.: Golem, 1970.
Borwein, J. and Peter Borwein, Pi and the AGM, New York: John Wiley, 1987.
Davis, P.J., The Long, Long Trail of Pi. In The Lore of Large Numbers, Chapter 17. New York: Random House, 1961.
Dieudonné, J., Abrégé d’histoire des mathématiques I, Paris: Hermann, 1978 (especially pp. 283 ff).
Schneider, Th., Einführung in die transzendenten Zahlen, Grundl. Math. Wiss., Springer-Verlag, 1957.
Siegel, C.L., Transzendente Zahlen, BI Hochschultaschenbuch 137, Mannheim, 1967.
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Remmert, R. (1991). What is π?. In: Numbers. Graduate Texts in Mathematics, vol 123. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1005-4_6
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DOI: https://doi.org/10.1007/978-1-4612-1005-4_6
Publisher Name: Springer, New York, NY
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