"Theory of Surfaces"

Japanese: 《曲面論》 - きょくめんろん

… CF Gauss is a mathematician who stands on the boundary between these two centuries. He became the director of the observatory at the University of Göttingen, and was personally involved in observations. He made notable achievements in the application of mathematics to astronomy, geodesy, electromagnetism, and other fields. In connection with these, he also opened up new frontiers in pure mathematics, such as by establishing a mathematical foundation for the least squares method and developing surface theory and potential theory. It is said that at the age of 19, he decided to become a mathematician after discovering that a regular heptadecagon could be constructed using a ruler and compass. …

From Darboux

…The method of moving frame that he invented had a great influence on 20th century geometry, and its contribution is immeasurable. The timeless classic, Theory of Surfaces, which took about 10 years to write, is a compilation of his achievements and those of his predecessors, and in particular, it discusses problems related to deformation of surfaces, spherical representation, surfaces of constant curvature, orthogonal families of surfaces, infinitesimal deformations, and so on, centering on partial differential equations, and beautifully captures various relationships. [Morimoto Akihiko] …

*Some of the terminology explanations that refer to "Surface Theory" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…　C.F.ガウスは両世紀の境界に立つ数学者である。彼はゲッティンゲン大学の天文台長となって，みずから観測にも従事して，天文学，測地学，電磁気学など数学の応用にも著しい功績があったが，それに関連して最小二乗法を数学的に基礎づけたり，曲面論，ポテンシャル論を展開するなど，純粋数学の新生面をも開いた。彼は19歳のとき，正十七角形が定規とコンパスで作図できることを発見して数学者となる決意をしたといわれる。…

【ダルブー】より

…彼が創案した動標構の方法は20世紀の幾何学にも大きな影響を与え，その寄与は計り知れない。約10年の歳月をかけて書かれた不朽の名著《曲面論》には彼の業績とその先駆者たちの仕事が凝集されており，なかでも曲面の変形，球面表示，定曲率曲面，直交曲面族，無限小変形などについての諸問題が偏微分方程式を軸として論ぜられ，種々の関連性がみごとにとらえられている。【森本明彦】。…

※「《曲面論》」について言及している用語解説の一部を掲載しています。

出典｜株式会社平凡社世界大百科事典第２版について | 情報

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