Geometric Construction of the Square Root Spiral

This GeoGebra example demonstrates the geometric construction of the Square Root Spiral (also known as the Spiral of Theodorus), visually representing the cumulative lengths of square roots of consecutive integers. The core mathematical concepts involved include real numbers, square roots, the Pythagorean theorem (where each step constructs a right triangle with legs of length 1 and √n, yielding a hypotenuse of √(n+1)), and basic vector geometry. To construct this, the example utilizes key GeoGebra commands such as Segment, OrthogonalLine, Circle, Intersect, and Polygon to iteratively build perpendicular triangles and trace their vertices. It is highly suitable for high school or introductory college students learning about real numbers, radicals, and the visual connection between algebra and geometry.