Radical Numbers Construction by Ramesses R.

①This example demonstrates how to geometrically construct radical numbers (like √2, √3) on a number line using straightedge-and-compass methods, visually proving the existence of irrational lengths. ②Core mathematical concepts include irrational numbers, the Pythagorean theorem, geometric construction, points and segments on a number line, and the recursive construction of square-root lengths. ③Construction details: Based on the summary, the GeoGebra commands used are Point, Segment, Circle, Intersect, Line, and Polygon, with objects A, B, f, c, d, D, C, g, E, poly1, b, c_1, and e. The process typically involves drawing perpendicular segments, using circles to transfer lengths, and intersecting lines to obtain successive radical lengths. ④This is suitable for upper middle school or high school students, ideal for classroom demonstrations on irrational numbers, geometric construction, or connecting algebra with geometry.