But what did he gain from it?
-
-
-
A cool gif and a shout out on twitter 350 years later.
- 1 more reply
New conversation -
-
-
The silk on a spider's web forming multiple elastic catenaries.pic.twitter.com/MAxDTB2Uqz
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
maybe Jungius was inspired by ants https://twitter.com/boni_bo/status/1026067216360501248 …
This Tweet is unavailable.Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
What's the Shape of a Hanging Chain? https://tfgorbe.wordpress.com/2015/05/27/whats-the-shape-of-a-hanging-chain/ … via @tfgorbe
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
A cosh. Which Newton later proved to also be a brachystochrone : curves that have the fastest falling object from a to b.
-
The brachistochrone curve is a cycloid (not a cosh).
- 1 more reply
New conversation -
-
-
The catenary is basically a hyperbolic cosine, cosh(x) = (eˣ+e⁻ˣ)/2, which for small x is approximately 1+½x².
-
It's a sinh to show that.
End of conversation
New conversation -
-
-
Joachim Jungius (1587–1657) proved that a homogeneous chain hanging under gravity would be a catenary BUT NOT in 1669. Its properties were first studied by Hooke. In 1691, Leibniz, Huygens and Johann Bernoulli showed that was a hyperbolic cosine.
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.