Positions of cards while shuffling (in a standard deck of 52 cards)

①This example dynamically visualizes the position changes of each card in a standard 52-card deck during shuffling, using points in 3D vector space to illustrate the randomness and permutation patterns. ②Core mathematical concepts include combinatorics (permutations and arrangements), 3D vectors, limits (as shuffle count approaches infinity, position distribution tends to uniformity), and continuity (smooth transitions of positions with shuffle steps). ③Construction details: GeoGebra commands such as If for conditional shuffle logic, TableText for generating card position tables, and LaTeX for mathematical typesetting; objects include points A1-A9, B1-B9, line l1, text labels text1-text4, and function f. ④Suitable for high school to undergraduate students studying combinatorics, probability, or 3D vector applications, and useful for math demonstrations or teaching materials to reveal the mathematical essence of shuffling algorithms.