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The picture seems meaningless without axes. The zero value of the first derivative could be anywhere depending on the rotation.--Frozenport (talk) 20:11, 27 July 2009 (UTC)
The curvature is invariant under rotations, and it's the first derivative of curvature we're talking about. Also, we can use Chapter 4 of http://www.math.psu.edu/tabachni/Books/BookPro.pdf as a citation. I don't really edit Wikipedia so I'll leave it up to you all. —Preceding unsigned comment added by 72.215.217.76 (talk) 16:24, 5 October 2010 (UTC)
Unclear link edit
The section 'Cusps and osculation beging with this sentence:
"Vertices are points where the curve has 4-point contact with the osculating circle at that point."
But the linked article never uses the terminology that it's linked from!!!
So: The phrase "4-point contact" needs to be replaced by the correct order of contact as defined in the linked article.
I hope someone knowledgeable about this subject will take care of this.