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Re: Stick shadows and sundial curves
From: Adrian F
Date: 2021 May 31, 05:41 -0700
From: Adrian F
Date: 2021 May 31, 05:41 -0700
Frank said : "Cone intersects flat plane... What do you get? Conic sections... of course! So that means that the shadow of the tip of the stick will trace out a circle, or an ellipse, or a parabola, or a hyperbola. ........[snip]...............When would you get a perfect parabolic shadow curve?"
From the diagram provided by Frank of the "double cones", I'm inclined to think the path of the shadow would become a parabola when the stick is located at latitude 51.2°N.
I went about the question in the original post by the inelegant method of plotting the path of the shadow of the tip, for latitudes 90°, 80°, 70°, 60° N. My circle and ellipses are attached.
AdrianF
