Perimeter of Ellipse/Approximation

Theorem

Let $K$ be an ellipse whose major axis is of length $2 a$ and whose minor axis is of length $2 b$.


The perimeter $\PP$ of $K$ can be approximated by the formula:

$\PP \approx 2 \pi \sqrt {\dfrac {a^2 + b^2} 2}$


Proof


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Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 4$: Geometric Formulas: Ellipse of Semi-major Axis $a$ and Semi-minor Axis $b$: $4.23$
  • 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 7$: Geometric Formulas: Ellipse of Semi-major Axis $a$ and Semi-minor Axis $b$: $7.23.$
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