Diana the Huntress and curve-fitting

Diana the Huntress was created by Anna Hyatt Huntington in 1934.

Diana
Diana

The sculpture was moved recently, and the guardrail was added very recently (this week, I think). Walking around it, one can clearly see that the guardrail is not round. What shape does it have? Direct measurements are difficult because the sculpture gets in the way.

It is natural to conjecture that the shape is an ellipse. A wonderful property of the ellipse is that it remains an ellipse in any perspective. This is despite the fact that the rectangle bounding the ellipse can be projected into an arbitrary convex quadrilateral.

Thus, the conjecture can be tested directly on the photograph: if the curve is an ellipse, then its original form is also an ellipse. And conversely. Since the rail has nonzero thickness, I worked with its upper outer edge. The ratio of major axes was measured at {b/a\approx 0.454} which corresponds to the eccentricity {e=\sqrt{1-(b/a)^2}\approx 0.89}. Also, the angle between the major axis and the horizontal line was measured at {\approx 0.0956} radian.

I created such an ellipse in fooplot using the polar form {\displaystyle r=\frac{a(1-e^2)}{1+e\cos (\theta-\theta_0)}}.

Ellipse
Ellipse

After adjusting the pixel size, it fit the outer edge very well:

Does it fit?
Does it fit?

And this is how math solves Real World Problems.