Euclid's Muse

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Caustic curve as focus of parabola

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Phil Todd



The red curve is f(x) (for -2≤x≤2).  The blue curve is the terms up to the square term of the Taylor series.  A is the vertex of this parabola, B is its focus. The orange curve is the caustic – envelope of the reflection of vertical rays reflected in a mirror aligned with f(x). Observe that the focus of the parabola traces the caustic.

Tags: caustic, Taylor-series, parabola
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