3次方程式の還元不能な場合
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- 長田, 直樹
- 東京女子大学
書誌事項
- タイトル別名
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- Cubic equations in the casus irreducibilis (Study of the History of Mathematics 2022)
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抄録
When a real cubic equation has three distinct real roots, it is called the casus irreducibilis or the case of irreducible. To find the roots of such equations using Cardano's formula, it is necessary to extract cube roots of imaginary binomials. In this paper we review remarkable works from Cardano to Euler on the solution of cubic equations in the casus irreducibilis and on the extraction of the cube roots of imaginary binomials. In it we give new proofs of Girard's method of constructing three real roots of a cubic equation and of Newton's method of extracting cube roots of imaginary binomials.
収録刊行物
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- 数理解析研究所講究録別冊
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数理解析研究所講究録別冊 B92 1-24, 2023-07
Research Institute for Mathematical Sciences, Kyoto University
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詳細情報 詳細情報について
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- CRID
- 1050297272079682816
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- NII書誌ID
- AA12196120
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- HANDLE
- 2433/284812
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- ISSN
- 18816193
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- 本文言語コード
- ja
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- 資料種別
- departmental bulletin paper
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- データソース種別
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- IRDB