The Tradition of Large Integers in Historical Arithmetical Textbooks.
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| Title: | The Tradition of Large Integers in Historical Arithmetical Textbooks. |
|---|---|
| Authors: | Brückler, Franka Miriam1 bruckler@math.hr, Stilinović, Vladimir1 vladimir.stilinovic@chem.pmf.hr |
| Source: | Mathematics Enthusiast. Feb2024, Vol. 21 Issue 1/2, p54-70. 17p. |
| Subject Terms: | *Decimal system, *Electronic textbooks, *Textbooks, Integers, Number systems, History of mathematics, Arithmetic |
| Geographic Terms: | Europe |
| Abstract: | After the Hindu-Arabic decimal positional system was introduced in Europe, throughout many centuries textbooks on elementary arithmetic, intended for beginners, had a more or less fixed organization of content, usually starting with chapters on numeration. These chapters, as a rule, contained one or more examples of large integers the purpose of which was simply to be named (read out loud), sometimes also vice versa. This tradition apparently began with the two first texts that significantly contributed to the spread of the decimal system in Europe--the Latin translations of al-Khwarizmi's treatise on decimal arithmetic, and Leonardo's Liber Abaci, containing examples of reading a 16-digit and a 15-digit number respectively. Throughout the centuries, the order of magnitude of these introductory numbers increased, in general up to some 30 digits, but in some cases to over 60 digits. In this paper we examine the development and extent of this characteristic of introductory arithmetic textbooks from the period 13th-19th century, and the conditions which lead to this, now extinct, practice. [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: 173884992 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The Tradition of Large Integers in Historical Arithmetical Textbooks. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Brückler%2C+Franka+Miriam%22">Brückler, Franka Miriam</searchLink><relatesTo>1</relatesTo><i> bruckler@math.hr</i><br /><searchLink fieldCode="AR" term="%22Stilinović%2C+Vladimir%22">Stilinović, Vladimir</searchLink><relatesTo>1</relatesTo><i> vladimir.stilinovic@chem.pmf.hr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+Enthusiast%22">Mathematics Enthusiast</searchLink>. Feb2024, Vol. 21 Issue 1/2, p54-70. 17p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Decimal+system%22">Decimal system</searchLink><br />*<searchLink fieldCode="DE" term="%22Electronic+textbooks%22">Electronic textbooks</searchLink><br />*<searchLink fieldCode="DE" term="%22Textbooks%22">Textbooks</searchLink><br /><searchLink fieldCode="DE" term="%22Integers%22">Integers</searchLink><br /><searchLink fieldCode="DE" term="%22Number+systems%22">Number systems</searchLink><br /><searchLink fieldCode="DE" term="%22History+of+mathematics%22">History of mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Arithmetic%22">Arithmetic</searchLink> – Name: SubjectGeographic Label: Geographic Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Europe%22">Europe</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: After the Hindu-Arabic decimal positional system was introduced in Europe, throughout many centuries textbooks on elementary arithmetic, intended for beginners, had a more or less fixed organization of content, usually starting with chapters on numeration. These chapters, as a rule, contained one or more examples of large integers the purpose of which was simply to be named (read out loud), sometimes also vice versa. This tradition apparently began with the two first texts that significantly contributed to the spread of the decimal system in Europe--the Latin translations of al-Khwarizmi's treatise on decimal arithmetic, and Leonardo's Liber Abaci, containing examples of reading a 16-digit and a 15-digit number respectively. Throughout the centuries, the order of magnitude of these introductory numbers increased, in general up to some 30 digits, but in some cases to over 60 digits. In this paper we examine the development and extent of this characteristic of introductory arithmetic textbooks from the period 13th-19th century, and the conditions which lead to this, now extinct, practice. [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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.54870/1551-3440.1617 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 54 Subjects: – SubjectFull: Decimal system Type: general – SubjectFull: Electronic textbooks Type: general – SubjectFull: Textbooks Type: general – SubjectFull: Integers Type: general – SubjectFull: Number systems Type: general – SubjectFull: History of mathematics Type: general – SubjectFull: Arithmetic Type: general – SubjectFull: Europe Type: general Titles: – TitleFull: The Tradition of Large Integers in Historical Arithmetical Textbooks. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Brückler, Franka Miriam – PersonEntity: Name: NameFull: Stilinović, Vladimir IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 15513440 Numbering: – Type: volume Value: 21 – Type: issue Value: 1/2 Titles: – TitleFull: Mathematics Enthusiast Type: main |
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