{"slug":"equations-that-changed-the-world","title":"The Equations That Changed the World","description":"Explore 17 equations that shaped mathematics, physics, and our understanding of the universe.","progress_percent":0,"tone":"friendly","lessons":[{"id":1,"title":"Pythagoras's Theorem","objective":"Show that the two smaller square areas combine into the area on the hypotenuse.","steps":["Resize the legs of a right triangle.","Watch the attached squares change area.","See that a² + b² always equals c²."],"duration_minutes":12,"sort_order":1}]}