**Catenary**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.

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**Source>>** http://mathworld.wolfram.com/Catenary.html►

**Animation via mathani>>** http://mathani.tumblr.com/#catenary #mathematics #animations