포락선 연구의 역사와 포락선의 여러 가지 정의 = History of Studies on the Envelope Curves and Various Definitions of the Envelope

국문 초록 (Abstract)

광선의 포락선인 초면(caustic)에 관한 연구는 17세기 호이겐스 등의 기하적 광학 연구에서 시작되었다. 17세기에 광학에서 가장 중요한 문제의 하나가 태양 광선을 초점에 모으는 것이었고, 이는 당시의 여러 실용적인 광학기구 제작을 위하여 해결해야 하는 문제였다. 이 시기 초면에 대한 연구로부터 시작하여 19세기까지 포락선에 대한 개념이 일반화되고 다양한 분야로 확장되었다. 본 논문에서는 포락선 곡선 연구에 관련된 수학적 역사를 살펴보고 포락선을 정의하는 몇 가지 방법을 비교하여 그에 따라 포락선을 구하는 예을 제시한다.

다국어 초록 (Multilingual Abstract)

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.

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