As a bernoulli_brachistochrone seems an inverted cycloïd







And seems there is yet a Cycloïd somewhere... http://moi3d.com/forum/index.php?webtag=MOI&msg=6149.1

formula for Bemfarmer
https://mathsbyagirl.wordpress.com/2016/07/27/brachistochrone-curve-problem/

some geometric curves by Bemfarmer http://moiscript.weebly.com/geacuteomeacutetries-par-bemfarmer.html

from http://www.nanotechinnov.com/architecture-03-brachistochrone-et-chainette