Spiral of Theodorus (Square Root Spiral)

This example demonstrates the Square Root Spiral, also known as the Spiral of Theodorus, created by the ancient Greek mathematician Theodorus. The spiral consists of a sequence of adjacent right triangles with leg lengths of 1, √2, √3, √4...√n, forming a continuous rotating spiral structure. Core mathematical concepts include the Pythagorean theorem (each pair of adjacent triangles forms a right triangle), geometric representation of square roots, the increasing pattern of tangent function, and cumulative angle measurement. Construction: Although the summary shows only a text1 object, the graphic is essentially generated through iteration, where each new triangle uses the hypotenuse of the previous triangle as one leg while keeping the other leg at length 1, ensuring all triangles are right triangles without overlap. Suitable for upper middle school students to understand the relationship between the Pythagorean theorem and trigonometric functions, or as a classic case for mathematics teaching combining numbers and shapes.