Bibliographic Details
| Title: |
The Figurate Numbers: From Verbal Expression to Algebraic Symbolism. |
| Authors: |
Lodder, Jerry1 jlodder@nmsu.edu |
| Source: |
Mathematics Enthusiast. Jun2025, Vol. 22 Issue 1/2, p45-80. 36p. |
| Subject Terms: |
*Generative grammar, *Mathematics education (Primary), *Historical source material, Polygonal numbers, Discrete mathematics |
| Abstract: |
We study the historical development of the figurate numbers, from ancient Greece through Pierre de Fermat to the work of Blaise Pascal, examining key passages for the construction and computation of the figurate numbers as well as their use in enumerating combinations. To assist in a transition to algebraic equivalents of these verbal passages, we introduce tools from transformational grammar to rewrite the surface structure of certain sentences in terms of more streamlined sentences amenable to algebraic formation. These linguistic techniques allow for the identification of key nouns that become single algebraic symbols, while other linguistic rules show how these nouns are modified either by algebraic operations or by the inclusion of modern-day subscripts. The material can be adapted for a number of undergraduate mathematics classroom settings, e.g., general education courses, college algebra, discrete mathematics. [ABSTRACT FROM AUTHOR] |
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| Database: |
Education Research Complete |
