{"id":1,"slug":"pythagorass-theorem","title":"Pythagoras's Theorem","formula":"a^2 + b^2 = c^2","author":"Pythagoras","year":"530 BC","category":"geometry","description":"The fundamental relationship between the sides of a right triangle.","stage":"live-demo","hook":"You need to build a ramp. The step is 3 feet high, the base starts 4 feet away. How long is the ramp?","hook_action":"Drag the sides of the triangle to see a² + b² always equals c².","variables_data":[{"max":12,"min":1,"name":"a","step":0.5,"unit":null,"color":"primary","symbol":"a","default":3,"description":"Vertical side"},{"max":12,"min":1,"name":"b","step":0.5,"unit":null,"color":"secondary","symbol":"b","default":4,"description":"Horizontal side"},{"max":20,"min":0,"name":"c","step":0.01,"unit":null,"color":"result","symbol":"c","default":5,"constant":true,"description":"Hypotenuse (computed)"}],"presets_data":[{"label":"3-4-5","values":{"a":3,"b":4}},{"label":"5-12-13","values":{"a":5,"b":12}},{"label":"Ladder","values":{"a":2,"b":6}}],"lessons_data":[{"id":"touch","hint":"Find the blue handle at the top of side a.","insight":"The hypotenuse c grew too. The squares always balance: a² + b² = c².","unlocked":["a"],"celebration":"subtle","instruction":"Grab the blue dot on side a and drag to make it longer.","successType":"variable_changed","successTarget":"a"},{"id":"squares","insight":"a² + b² = c². Always. No matter what size.","unlocked":["a","b"],"celebration":"subtle","instruction":"Watch the squares. Blue + amber always equals red. Drag both a and b.","successType":"variable_changed","successTarget":"b"},{"id":"classic","insight":"c = 5. The famous 3-4-5 triangle. Builders have used this for 4,000 years.","unlocked":["a","b"],"celebration":"big","instruction":"Set a = 3 and b = 4. What is c?","successType":"value_reached","successValue":3,"successTarget":"a","successTolerance":0.5}],"glossary_data":[{"color":"#ef4444","words":["hypotenuse"],"tooltip":"The longest side, opposite the right angle","highlightClass":"sq-c"},{"color":"#64748b","words":["right angle","right triangle"],"tooltip":"The 90° corner","highlightClass":"right-angle"},{"color":"#8b5cf6","words":["square","squares","area"],"tooltip":"Area squares attached to each side","highlightClass":"all-squares"},{"color":"#334155","words":["triangle"],"tooltip":"The right triangle","highlightClass":"tri"},{"color":"#ef4444","words":["ramp"],"tooltip":"The ramp length equals the hypotenuse","highlightClass":"sq-c"}]}