Geometric Visualization of Integer Addition: From Vectors to Intersections

This example demonstrates integer addition through a geometry-based construction: it uses vector displacement to encode how adding integers moves from one point to another, and then reveals the corresponding result via intersection and median/midpoint positions in the drawn configuration. The key math ideas include the interpretation of integer sums as repeatable geometric moves, vector addition and its geometric meaning, intersection of constructed geometric entities, and using midpoint/median concepts to encode or extract the resulting value. Construction-wise, the GeoGebra commands reflected in the provided construct summary are Point, Random, Vector, and Textfield. The involved objects (e.g., f, g, A, B, a, b, C, D, u, v) support the creation of reference points and the vectors u and v that represent the addends, while UI elements such as button1/button2 and InputBox1 with associated text fields (text1, text2, etc.) allow the user to input parameters and trigger updates to see the sum visually. Suitable for middle school through early undergraduate levels, especially for teaching vector/coordinate geometry, number–geometry connections, and interactive geometric construction tasks.