A rope is supported at its ends. What shape do you think it assumes?Galileo
, some 400 years ago, thought a parabola
(red, thin line). He was wrong: the right answer is a so-called catenary
(black), which, however, resembles a parabola quite well!
The curve a hanging flexible wire or chain assumes when supported at its ends and acted upon by a uniform gravitational force. The word catenary is derived from the Latin word for "chain".
In 1669, Jungius
disproved Galileo's claim
that the curve of a chain hanging under gravity would be a parabola.
The curve is also called the alysoid and chainette
. The equation was obtained by Leibniz, Huygens, and Johann Bernoulli in 1691
in response to a challenge by Jakob Bernoulli.Huygens
was the first to use the term catenary in a letter to Leibniz
in 1690, and David Gregory
wrote a treatise on the catenary in 1690. If you roll a parabola along a straight line, its focus traces out a catenary.
As proved by Euler
in 1744, the catenary is also the curve which, when rotated, gives the surface of minimum surface area (the catenoid
) for the given bounding circle.
► Source>> http://mathworld.wolfram.com/Catenary.html
► Animation via mathani>> http://mathani.tumblr.com/#catenary #mathematics #animations