長岡亮介数学勉強会「A History of Abstract Algebra by I.Kleiner」 第4回(p5-7)

レポート https://akasakas.cool/wp-content/uploads/2020/05/第4回1.4-Cubic-and-quartic-equations20190326勉強会.pdf

1 History of Classical Algebra
1.4 Cubic and quartic equations 3次、4次の方程式

カルダーノは1545年に著した本『偉大なる術(アルス・マグナ)』(ラテン語: Ars magna de Rebus Algebraicis) のなかで3次方程式の根の公式、4次方程式の解法を示した。

BC16世紀までに2次方程式を解していたのに、3次方程式が解けたのはそれから3,000年も費やしたのだ。x3乗 = ax + bという3次方程式の解は、カルダーノの公式(タルタリアによって発見されていたものだが)として呼ばれるものだ。
(i) カルダーノは記号を全然使わなかった。
(ii) 彼は、通常、3次方程式の一つの根を見つけることでいつも満足した。
(iii) 負の数は時々発見されるけれども、それらを“fictitious”(虚数)と呼んで、疑った。
(iv) 3次方程式の解法手順に幾何学根拠を与えた。

21歳年上のカルダーノの召使いとして働いていたフェラーリは、4次方程式の多項式のベキ根による解法を発見した。

16世紀イタリアに3人の数学者が生きていた。フェラーリは1565年に43歳で毒殺され、カルダーノは1576年に75歳で自殺した。もう一人はボンベリである。


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