Ladder against the wall: Pythagorean theorem dynamic demo

① This example demonstrates the Pythagorean theorem through a ladder leaning against a wall, visually showing the relationship between the squares of the two legs and the hypotenuse in a right triangle. ② Core mathematical concepts include the Pythagorean theorem, right triangles, vectors, perpendicular lines, and continuous variation. ③ Construction highlights: using GeoGebra commands such as Segment, Point, OrthogonalLine, and UnitVector, with objects like A, B, a, Ladder, r, b, u, resi, O, d, Window, leiter, F, h, and s to build an interactive model where the ladder's position can be adjusted. ④ Suitable for middle school to high school students learning the Pythagorean theorem, and for teachers to demonstrate or students to explore the geometric and algebraic connections between side lengths.