Curve Stitching: Constructing a Parabola from Straight Lines (1)

① This example demonstrates how a parabola-like curve can be constructed using only straight line segments, following simple connection rules, visually showing the envelope of lines approximating a smooth curve. ② Core mathematical concepts include the tangent envelope of a parabola, sequences and iteration, limit intuition, and foundations of continuity and integral calculus. ③ Construction details: The GeoGebra commands involve Sequence to generate points and segments, with objects such as n (iteration count), a (parameter), list1, list4, list5, list2, list3 (lists of points or segments), A (key point), b, c (auxiliary objects), and text1 (label). A slider controls n to observe how the approximation improves. ④ Suitable for high school to early college students, useful for geometry construction, function graphing, and pre-calculus teaching, as well as math lab or inquiry activities.