The Figurate Numbers: From Verbal Expression to Algebraic Symbolism.
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| 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] |
| Copyright of Mathematics Enthusiast is the property of Prof. Bharath Sriraman and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Education Research Complete |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 180183945 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The Figurate Numbers: From Verbal Expression to Algebraic Symbolism. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Lodder%2C+Jerry%22">Lodder, Jerry</searchLink><relatesTo>1</relatesTo><i> jlodder@nmsu.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+Enthusiast%22">Mathematics Enthusiast</searchLink>. Jun2025, Vol. 22 Issue 1/2, p45-80. 36p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Generative+grammar%22">Generative grammar</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematics+education+%28Primary%29%22">Mathematics education (Primary)</searchLink><br />*<searchLink fieldCode="DE" term="%22Historical+source+material%22">Historical source material</searchLink><br /><searchLink fieldCode="DE" term="%22Polygonal+numbers%22">Polygonal numbers</searchLink><br /><searchLink fieldCode="DE" term="%22Discrete+mathematics%22">Discrete mathematics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics Enthusiast is the property of Prof. Bharath Sriraman and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=ehh&AN=180183945 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.54870/1551-3440.1651 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 36 StartPage: 45 Subjects: – SubjectFull: Generative grammar Type: general – SubjectFull: Mathematics education (Primary) Type: general – SubjectFull: Historical source material Type: general – SubjectFull: Polygonal numbers Type: general – SubjectFull: Discrete mathematics Type: general Titles: – TitleFull: The Figurate Numbers: From Verbal Expression to Algebraic Symbolism. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Lodder, Jerry IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 15513440 Numbering: – Type: volume Value: 22 – Type: issue Value: 1/2 Titles: – TitleFull: Mathematics Enthusiast Type: main |
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