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Discovering the cosine law via calculus

 

作者: DavidE. Dobbs,  

 

期刊: International Journal of Mathematical Education in Science and Technology  （Taylor Available online 1986）
卷期: Volume 17, issue 5  

页码: 623-658

 

ISSN:0020-739X

 

年代: 1986

 

DOI:10.1080/0020739860170512

 

出版商: Taylor & Francis Group

 

数据来源: Taylor

 

摘要:

Heuristic arguments are given to explain the presence of the term ‐‐2bccos a in the cosine law. The arguments presuppose the sine law and Pythagoras's theorem. The explanation hinges on the mean value theorem of differential calculus, since the triangle in question is viewed as resulting from a perturbation of a suitable right triangle.

 

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