次元の同次性
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定義
物理的に有効な方程式のすべての項が同一の次元を持つ必要があるという要件で、異なる種類の量が加算または等号で結ばれることを禁ずる。
解説
In the kinematic equation v² = u² + 2as, every term has dimensions of [length]²[time]⁻² (m²/s²): v² is (m/s)², u² is (m/s)², and 2as is (m/s²)(m) = m²/s². Adding a term in meters would violate dimensional homogeneity and expose a derivation error. This principle, formalized by Fourier in 1822, is the basis of dimensional analysis and a powerful error-checking tool.
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