{"success":true,"data":{"calculator":{"name":"Area of Circle Calculator","version":"2.0","description":"Advanced circle area calculator supporting multiple input methods with educational content and AI platform optimization","category":"Mathematics / Geometry"},"inputTypes":[{"id":"radius","name":"Radius","unit":"units","formula":"A = πr²","constraints":{"min":0.0001,"max":null,"type":"positive number"}},{"id":"diameter","name":"Diameter","unit":"units","formula":"A = πd²/4","constraints":{"min":0.0001,"max":null,"type":"positive number"}},{"id":"circumference","name":"Circumference","unit":"units","formula":"A = C²/(4π)","constraints":{"min":0.0001,"max":null,"type":"positive number"}}],"outputFormat":{"value":"area","unit":"square units","precision":15,"format":"decimal number"},"mathematicalBackground":{"constantsPi":3.14159265358979,"historicalContext":"Ancient mathematicians including Archimedes proved that the area of a circle equals half its circumference times its radius, establishing the foundation for the modern formula A = πr².","derivation":"The formula A = πr² can be derived through integral calculus by integrating the circumference (2πr) from 0 to radius r, or by dividing a circle into infinite triangular wedges."},"apiEndpoints":[{"path":"/api/calculate","method":"POST","description":"Calculate circle area with detailed steps","example":"POST /api/calculate\n{\"value\": 10, \"inputType\": \"radius\"}"},{"path":"/api/calculate","method":"GET","description":"Calculate circle area using query parameters","example":"GET /api/calculate?value=10&type=radius"},{"path":"/api/metadata","method":"GET","description":"Retrieve calculator metadata and features","example":"GET /api/metadata"},{"path":"/api/specs","method":"GET","description":"Get complete calculator specifications","example":"GET /api/specs"},{"path":"/api/schema","method":"GET","description":"Retrieve JSON-LD schema for SEO","example":"GET /api/schema"}],"accessibilityFeatures":["Semantic HTML structure","ARIA labels for form inputs","Keyboard navigation support","High contrast color scheme","Mobile-responsive design","Text alternatives for all visuals","API documentation for programmatic access"],"performanceMetrics":{"responseTime":"<100ms","cacheControlMaxAge":86400,"supportsCORS":true}}}