nTautochrone(Math) A curved line, such that a heavy body, descending along it by the action of gravity, will always arrive at the lowest point in the same time, wherever in the curve it may begin to fall; as, an inverted cycloid with its base horizontal is a tautochrone
Century Dictionary and Cyclopedia
ntautochroneIn mathematics, a curve line such that a heavy body descending along it by gravity will, from whatever point in the curve it begins to descend, always arrive at the lowest point in the same time. The cycloid possesses this property for a constant force with no resistance.
Webster's Revised Unabridged Dictionary
Gr. , for the same + time: cf. F. tautochrone,
The mechanical properties of the cycloid were investigated by Christiaan Huygens, who proved the curve to be tautochronous.
"Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 8" by Various