Quote:
Originally Posted by Ether
... a dialog is most welcome. Please do post your thoughts and ideas.
The purpose of these quizzes is to start a conversation from which both participants and readers can gain insight. The journey is as important as the goal.
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Thanks.
Ok, so here's what i've got:
The problem statement says a coordinate system exists, but it doesn't state if it's Cartesian, or polar, or maybe even something else. The equation is "simple" but something simple in a polar coordinate system can be complex in a Cartesian one. It's also undetermined what the origin of said system is.
I know it's not a circle (polar, r=constant). The perpendicular bisectors of each adjacent point segment aren't close to intersecting at a single point.
I tried rotating the points to get a good fit on a parabola, which would have a relatively simple equation, assuming the origin was on the vertex. The best I got was around 142.5 degrees clockwise, but that didn't quite match up.
Also, the radius of curvature appears to be increasing from the starting point until the ending point.
Other observations:
The points are not equidistant in spacing. The minimum distance appears to be around the 5th or 6th point.
I couldn't find a rotation which places the x or y coordinate in equal spacing in Cartesian coordinates.