Abstract
Discovery of the incommensurability of the diagonal of the square sent a shock wave through Greek mathematics, and discredited Pythagorean metaphysics. However, the next logical extension of the same idea gave the Greeks a treasured geometrical concept, and a beautiful number to be handed down through the ages for our enjoyment today. To find this number, we only have to ask: what happens if, instead of a square, we consider a rectangle with sides equal to 1 and 2? Once the Greeks had considered the square with sides equal to one, it is only natural they would have extended this idea to look at the 1×2 rectangle.
Natural philosophy, mathematics and astronomy, carry the mind from the country to the creation, and give it a fitness suited to the extent.
Thomas Paine
Address to the People of England1
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End Notes
Thomas Paine, Address to the People of England (CD: DeskTop BookShop) (Indianapolis: WeMake CDs, Inc., 1994).
Carl B. Boyer, A History of Mathematics (New York: John Wiley and Sons, 1968), p. 55.
H.E. Huntley, The Divine Proportion (New York: Dover Publications, 1970), p. 62.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers (New York: Penguin Books, 1986), p. 37.
Boyer, A History of Mathematics, p. 281.
The Fibonacci Quarterly, Fibonacci Association c/o South Dakota State University Computer Science Department, Box 2201, Brookings, SD 57007–1596.
H.E. Huntley, The Divine Proportion, p. 160.
George Cheverghese Joseph, The Crest of the Peacock (London: Penguin Books, 1991), p. 197.
Jean L. McKechnie, ed., Webster’s New Twenthieth Century Dictionary of English Language (New York: Simon and Schuster, 1979), p. 1834.
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© 1996 Calvin C. Clawson
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Clawson, C.C. (1996). Exotic Connections. In: Mathematical Mysteries. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-6080-1_7
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DOI: https://doi.org/10.1007/978-1-4899-6080-1_7
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