Brāhmasphuṭasiddhānta: Difference between revisions
→Brāhmasphuṭasiddhānta rules for numbers: Removing this section as being WP:UNDUE |
restore a cut-down section about positive, negative and zero, which was referenced and clearly had encyclopedic value. if you think this is 'undue' weight, then please *add* material about the other contents of the book. |
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The book was written completely in verse and does not contain any kind of mathematical notation. Nevertheless, it contained the first clear description of the [[quadratic formula]] (the solution of the quadratic equation).<ref name=Bradley>Bradley, Michael. ''The Birth of Mathematics: Ancient Times to 1300'', p. 86 (Infobase Publishing 2006).</ref><ref>Mackenzie, Dana. ''[https://books.google.com/books?id=2QYSAAAAQBAJ&printsec=frontcover#v=onepage&q=Brahmagupta&f=false The Universe in Zero Words: The Story of Mathematics as Told through Equations]'', p. 61 (Princeton University Press, 2012).</ref> |
The book was written completely in verse and does not contain any kind of mathematical notation. Nevertheless, it contained the first clear description of the [[quadratic formula]] (the solution of the quadratic equation).<ref name=Bradley>Bradley, Michael. ''The Birth of Mathematics: Ancient Times to 1300'', p. 86 (Infobase Publishing 2006).</ref><ref>Mackenzie, Dana. ''[https://books.google.com/books?id=2QYSAAAAQBAJ&printsec=frontcover#v=onepage&q=Brahmagupta&f=false The Universe in Zero Words: The Story of Mathematics as Told through Equations]'', p. 61 (Princeton University Press, 2012).</ref> |
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== Positive and negative numbers== |
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''Brāhmasphuṭasiddhānta'' is one of the first books to provide concrete ideas on [[positive number]]s, [[negative number]]s, and zero.<ref>[[Henry Thomas Colebrooke]]. ''Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara'', London 1817, p. 339 ([https://archive.org/details/algebrawitharith00brahuoft online])</ref> For example, it notes that the sum of a positive number and a negative number is their difference or, if they are equal, zero; that subtracting a negative number is equivalent to adding a positive number; that the product of two negative numbers is positive. Some of the notions of fractions differ from the modern [[rational number]] system. For example, Brahmagupta allows [[division by zero]] resulting in a fraction with a {{math|0}} in the denominator, and defines {{math|1=0/0 = 0}}. In modern mathematics, division by zero is undefined for any [[field (mathematics)|field]].<ref name="Kaplan">{{cite book |
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| last = Kaplan | first = Robert | title = The Nothing that is: A Natural History of Zero |
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| url = https://archive.org/details/nothingthatisnat00kapl | url-access = registration | publisher = Oxford University Press | year = 1999 | location = New York |
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| pages = [https://archive.org/details/nothingthatisnat00kapl/page/68 68–75] | isbn = 0-19-514237-3}} |
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</ref> |
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==References== |
==References== |
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Revision as of 19:42, 2 January 2023
The Brāhmasphuṭasiddhānta ("Correctly Established Doctrine of Brahma", abbreviated BSS) is the main work of Brahmagupta, written c. 628.[1] This text of mathematical astronomy contains significant mathematical content, including a good understanding of the role of zero, rules for manipulating both negative and positive numbers, a method for computing square roots, methods of solving linear and quadratic equations, and rules for summing series, Brahmagupta's identity, and Brahmagupta theorem.
The book was written completely in verse and does not contain any kind of mathematical notation. Nevertheless, it contained the first clear description of the quadratic formula (the solution of the quadratic equation).[2][3]
Positive and negative numbers
Brāhmasphuṭasiddhānta is one of the first books to provide concrete ideas on positive numbers, negative numbers, and zero.[4] For example, it notes that the sum of a positive number and a negative number is their difference or, if they are equal, zero; that subtracting a negative number is equivalent to adding a positive number; that the product of two negative numbers is positive. Some of the notions of fractions differ from the modern rational number system. For example, Brahmagupta allows division by zero resulting in a fraction with a 0 in the denominator, and defines 0/0 = 0. In modern mathematics, division by zero is undefined for any field.[5]
References
- ^ "Brahmagupta | Indian astronomer". Encyclopedia Britannica.
- ^ Bradley, Michael. The Birth of Mathematics: Ancient Times to 1300, p. 86 (Infobase Publishing 2006).
- ^ Mackenzie, Dana. The Universe in Zero Words: The Story of Mathematics as Told through Equations, p. 61 (Princeton University Press, 2012).
- ^ Henry Thomas Colebrooke. Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara, London 1817, p. 339 (online)
- ^ Kaplan, Robert (1999). The Nothing that is: A Natural History of Zero. New York: Oxford University Press. pp. 68–75. ISBN 0-19-514237-3.
External links
- Brahmasphutasiddhanta at GRETIL (mathematical chapters: 12, 18-20, 21.17-23)
- O'Connor, John J.; Robertson, Edmund F., "Brahmagupta", MacTutor History of Mathematics Archive, University of St Andrews