Choosing an easement curve   Id like to be clear about a which curves are actually used in practice  b in the various railways administrations not just North American but also others eg Australian European Indian etc  This would help with NPOV  My main concern is with a  Although the article mostly discusses Euler spirals it seems to give the impression thats the only curve used under varying names  However consider this quotation from the AREMA reference in the article  There are several different types of mathematical spirals available for use including the clothoid the cubic parabola and the lemniscate  Of more common use on railways are the Searles the Talbot and the AREMA Chord spirals which are empirical approximations of true spirals   This reference is of course discussing common use on American railways but even in this limited context it appears there are at least three ideal mathematical spiral forms involved the clothoid the cubic parabola and the lemniscate along with various practical approximations to them  The article would ideally give the history of the use and adaptation of these various spiral forms  Doing so would provide a solid illustration of how technological innovation was both necessitated and encouraged by the Age of Rail  a valuable insight into the social impact of rail  Im guessing that the AREMA reference probably continues on from the quote above to give some further detail about those approximations their inventors and their history but it may not  In any case can anybody provide suitable references to help flesh out this story