• Journal for History of Mathematics
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• v.28 no.1
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• pp.31-44
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• 2015

The cycloid curve had been studied by many mathematicians in the period from the 16th century to the 18th century. The results of those studies played important roles in the birth and development of Analytic Geometry, Calculus, and Variational Calculus. In this period mathematicians frequently used the cycloid as an example to apply when they presented their new mathematical methods and ideas. This paper overviews the history of mathematics on the cycloid curve and presents proofs of its important properties.

• Journal for History of Mathematics
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• v.37 no.4
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• pp.93-105
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• 2024

Research on the caustic, the envelope of light rays, began with the geometric optics studies of Huygens and others in the 17th century. One of the most important problems in optics in the 17th century was focusing the sun's rays. This was a problem that had to be solved in order to manufacture various practical optical instruments at the time. Beginning with research on the caustic during this period, the concept of envelope became generalized and expanded to various fields until the 19th century. This paper examines the mathematical history involved in the study of envelope curves. We compare several methods of defining the envelope and provide an example of calculating the envelope accordingly.