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Caustic curves ‒ higher mathematics outside higher education. (English)
Stud. Sci. Fac. Paedagog. 15, No. 4, 216-226 (2016).
Summary: This paper presents the outline of an irregular lesson for secondary school students about classical and free shaped curves and their caustic curves. If we emit straight lines into a curve than the reflected rays are defining the caustic of the curve. In the secondary school the students are learning some special caustics, but their knowledge about this area is superficial. Our purpose is to show this discipline which requires higher mathematical knowledge for the students in an understandable way. We show the classical curves and their caustics which are not all news for the students and then we present a new type of curve, called Bézier curve. To find its caustic curve we present the standard envelope method and implement it into the curve. After than we present the way we can show the problem for the students with an interactive computer game. While they are playing they experience that the caustic curve conducts somehow else. To understand this behavior we present the geometric effect of the control points onto the caustic of the Bézier curve.
Classification: G70
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