Abstract
The old Chinese proverb, “A picture is worth a thousand words,” is true in mathematics. We frequently use geometric illustrations to clarify concepts and illustrate relationships in every branch of mathematics. Figurate Numbers provide such a link between number theory and geometry; they are positive integers that can be represented by geometric patterns. Although the Pythagoreans are usually given credit for their discovery, the ancient Chinese seem to have originated such representations about 500 years before Pythagoras. Many centuries later, in 1665, Pascal wrote a book on them, Treatise on Figurate Numbers.
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Notes
- 1.
See the Book of Revelation in the Bible.
- 2.
For Fibonacci enthusiasts, we note that 11 is a Lucas number and 89 a Fibonacci number; there are 1189 chapters in the Bible, of which 89 are in the New Testament.
- 3.
Mathematica Ⓡ is a registered trademark of Wolfram Research, Inc.
References
S. Assadulla, Problem 70.F, Mathematical Gazette 71 (1987), 66.
T. Koshy, Elementary Number Theory with Applications, Academic Press, 2nd edition, Burlington, MA, 2007.
T. Koshy, Triangular Arrays with Applications, Oxford, New York, 2011.
E.G. Landauer, On Squares of Positive Integers, Mathematics Magazine 58 (1985), 236.
R.B. Nelsen, Proofs Without Words, Mathematical Association of America, Washington, D.C., 2000.
R.B. Nelsen, Visual Gems of Number Theory, Math Horizons (Feb. 2008), 7–9, 31.
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Koshy, T. (2014). Triangular Numbers. In: Pell and Pell–Lucas Numbers with Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8489-9_5
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DOI: https://doi.org/10.1007/978-1-4614-8489-9_5
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