Nanson公式证明的诠注及一个新证明

A comment on proofs of Nanson's formula with a new proof

  • 摘要: 针对现行文献对Nanson公式证明的3种不同方法, 文章分别从数学演绎与力学概念明晰化的角度对3种证明的演绎过程及其特色进行了分析, 指出了相应的优劣之处以及各自需要改进的地方. 在此基础上, 文章给出了一个改进的易于理解的证明. 文章还提出了力学问题的演绎与证明应该充分反映力学规律的论点.

     

    Abstract: In terms of the three typical proofs for the Nanson’s formula nowadays in literatures, the paper evaluates the three proofs with their characteristics from a point of view of both mathematical deduction and limpiditazation of mechanical concepts, pointing out respectively for each proof the advantages and disadvantages together with the spots where improvements for the proofs may be made. Accordingly, the paper puts forward an improved and comprehensible proof for the formula. Also, the paper proposes an argumentation that a proof for a mechanical problem should reflect the intrinsic law of mechanics.

     

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