What Is an Ellipse Circumference Calculator?
An ellipse is a smooth, closed curve that generalizes the concept of a circle. It is defined by two principal axes:
- Semi-major axis (a): The longest radius, extending from the center to the edge along the longest dimension.
- Semi-minor axis (b): The shortest radius, extending from the center to the edge along the shortest dimension.
When a=b, the ellipse becomes a circle, and its circumference is simply 2πa. For ellipses where a≠b, however, the formula for the circumference is not as straightforward. While the exact perimeter (or circumference) of an ellipse is given by a complex integral with no closed-form solution, several approximations exist. One common approximation involves computing:
\[ \text{Circumference} \approx \pi \sqrt{2\left(a^2+b^2\right)} \]
This formula works perfectly for a circle (where a=b=r) and provides a quick estimate for an ellipse as well. Although there are more accurate approximations (like those developed by Ramanujan), our calculator uses this straightforward method to balance simplicity and performance.
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