Tiling the Plane with Two Squares: Construction and Translation Pattern

This example demonstrates how to tile the plane using two square tiles by designing local configurations and then repeating them through translation to obtain a seamless global covering. It focuses on geometric tiling (tessellation), translation symmetry/patterns, and the consistency conditions required for the squares to meet without gaps or overlaps. The construction also leverages right-triangle relationships and a structured organization using natural-number indexing to control how tile positions propagate. In GeoGebra, the model is built with the commands Point, Polygon, and Sequence: key vertices (A, B, C, D, E, F, G, etc.) define polygonal tile shapes (poly1, poly2), while Sequence-based objects (g, h, i, j, k, l, m, n, L_1) generate the repeated placements that extend the tiling across the plane. Suitable for advanced secondary students, geometry/construction instruction, and learners who want to connect visual construction with rigorous tiling logic.