Interactive Exploration of Pythagoras' Theorem and Vectors

This example demonstrates the verification of Pythagoras' Theorem in right triangles and explores vector representation and operations. It involves core mathematical concepts such as Pythagoras' Theorem, vector magnitude and dot product, centroid of a triangle, and the relationship between secant lines and circles. Construction highlights include using commands like Random, RandomElement for generating random data, Textfield for displaying text, Intersect for calculating intersections, and TableText for showing tabular data, with objects like a, d_1, c_1, b, a_1, c, g, h, A1, f, b_1, A1_1, B1_1, C_1, D_1, m, p, e, l, k, d, i, j, n, B_1, d_2, B, A, text2, C, text3_1, A2, B2. It is suitable for high school mathematics teaching, combining geometry and algebra to deepen understanding of vectors and analytical geometry.