Editing Curvature (section)

==History==
{{Expand section|date=October 2019}}
In ''Tractatus de configurationibus qualitatum et motuum,''<ref>{{citation |last=Clagett |first=Marshall |author-link=Marshall Clagett |title=Nicole Oresme and the Medieval Geometry of Qualities and Motions |year=1968 |publisher=University of Wisconsin Press |isbn=978-0-299-04880-8 |place=Madison, WI }}</ref> the 14th-century philosopher and mathematician [[Nicole Oresme]] introduces the concept of curvature as a measure of departure from straightness; for circles he has the curvature as being inversely proportional to the radius; and he attempts to extend this idea to other curves as a continuously varying magnitude.<ref>{{citation |last1=Serrano |first1=Isabel M. |last2=Suceavă |first2=Bogdan D. |author-link2=Bogdan Suceavă |year=2015 |title=A Medieval Mystery: Nicole Oresme's Concept of Curvitas |journal=Notices of the AMS |volume=62 |issue=9 |pages=1030–1034 |doi=10.1090/noti1275 |doi-access=free}}</ref>

The curvature of a [[differentiable curve]] was originally defined through [[osculating circle]]s. In this setting, [[Augustin-Louis Cauchy]] showed that the center of curvature is the intersection point of two infinitely close [[normal (geometry)|normal lines]] to the curve.<ref name="Cauchy">{{citation |last1=Borovik |first1=Alexandre |author-link1=Alexandre Borovik |last2=Katz |first2=Mikhail G. |author-link2=Mikhail Katz |year=2011 |title=Who Gave You the Cauchy–Weierstrass Tale? The Dual History of Rigorous Calculus |journal=Foundations of Science |volume=17 |issue=3 |pages=245–276 |arxiv=1108.2885 |doi=10.1007/s10699-011-9235-x }}</ref>