#catenary

boston area september 1959

trolleybus wires

when you hold your necklace loose

and flip it so it's like the picture on the right

it is the same with the arc on the bridge

When you hold a necklace loosely, it naturally hangs into a catenary curve. When you flip it vertically, you get the same shape as a suspension bridge arch, or even better, a catenary arch.

A bit detailed explanation incoming:

A hanging chain like a necklace forms a catenary, from the Latin catena, that means chain.

Mathematically, this curve is:

y = a cosh (x/a)

where cosh is the hyperbolic cosine.

When you flip the necklace vertically, you get the inverted catenary.

And it is the shape that perfectly distributes compressive forces.

In bridges or arches, that is the best structure it can have.

‘Catenary Waves,’