In geometry, congruent transformations in Euclidean space that do not involve inversion (called motions), i.e., the composition of rotations and translations, form a transformation group, called the group of motions. Because this is the fundamental transformation group of Euclidean space, it plays a fundamental role in the analysis of the physical world. Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information |
幾何学においては,ユークリッド空間で,裏返しを含まない合同変換 (これを運動という) ,つまり,回転と平行移動の合成は変換群になる。これを運動群という。これはユークリッド空間の基本的な変換群なので,物理的世界の解析にあたって基本的な役割を果すことになる。
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