Power Functions, Limits, Orthocenter, and Stochastic Process Example

①This example demonstrates a comprehensive mathematical construction in GeoGebra that integrates power functions, limits, orthocenter of a triangle, tree diagrams, and stochastic processes, showing dynamic interactions between function sequences and geometric objects. ②Core mathematical concepts include power functions, limits, triangle orthocenter, tree diagrams, and stochastic processes, highlighting the intersection of algebra, geometry, and probability. ③Construction details: From the summary, commands such as Element, Point, Vector, Textfield, and Zip are used, creating objects like unit, f_2, f_1, n, ops, O_n, f, a, b, ax1, ax2, s, D, A, B, C, u, v, text2, w, d, text3, InputBox1, InputBox2, D2, A2, B2, C2, rlist, zlist, z1list, E, F, LL, UL, G, H, axis1b, text1_1, and text1, involving input boxes, lists, coordinate axes, and text labels to build an interactive mathematical experiment environment. ④Suitable for high school to university-level teaching or self-study, this example is useful for exploring the geometric meaning of function limits, simulating stochastic processes, and investigating properties of geometric objects under dynamic changes, also serving as material for interdisciplinary project-based learning.