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    "Ellipse perimeter is Ramanujan I, not a complete elliptic integral",
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      "title": "ISO 80000-2:2019 Quantities and units — Mathematics",
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      "title": "S. Ramanujan — Modular Equations and Approximations to π (1914)",
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      "supports": "Exact ellipse perimeter L(a,b) = 4a E(k), with k² = 1−b²/a² and a ≥ b. A displayed elementary perimeter approximation is distinct from this exact elliptic-integral definition; the reference does not establish the approximation’s error or validate CalculatorX.",
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      "publisher": "National Institute of Standards and Technology"
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      "title": "Gilbert Strang, Calculus — Chapter 3: Applications of the Derivative (MIT OpenCourseWare)",
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      "url": "https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/mitres_18_001_f17_ch03.pdf",
      "supports": "Standard equations and focal geometry of axis-aligned conic sections, including translated equations and the ellipse’s semiaxes. Ellipse area and perimeter are supported by separate integral references. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.",
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      "publisher": "Wellesley-Cambridge Press; hosted by MIT OpenCourseWare"
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      "publisher": "Wellesley-Cambridge Press; hosted by MIT OpenCourseWare"
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