A catenary describes the curve adopted by a chain suspended from two points – gravity acting uniformly along its length. I have been trying to suss out the right curvature for the top rail of a new four poster bed and playing with chains has helped.
As you can see, the chain is slightly more curved in the middle than at the ends, like the steam bent lath of oak on top of it.
Catenary curves are important in architecture – particularly in bridge building – because of the way that they resist bending moments. Gaudi loved them so much, all the spires of his great cathedral, the Sagrada Familia in Barcelona, are based upon the catenary curve – here is his fantastic inverted string model complete with tiny sand bags… a spider’s web of catenary curves.
If you are curious there are many mathematical treatments of catenary curves and their analogies in nature (skeletons). You will find them everywhere if you care to look. The lovely ‘Winking Bridge’ across the Tyne in Gateshead, dogs on leads, electricity cables hanging from pylons…
I would be the first to admit that I am no mathematician, but I do love symmetry in natural forms. The completed Ruskin Sculpture – Mir Jansen and I will be exhibiting at the Millennium Gallery, consists of a framework of steam bent, thin oak laths on a sturdy base attached to a circular annulus to make a light, airy framework. Within the framework hang a series of paintings by Mir in gouache on panels of oak all cut from the same tree. The paintings appear to float within the interior of the sculpture, each suspended on 3 or 4 powerful magnets.
The laths are identical to the one in the top picture. They were bent over a hemispherical frame – the slight recoil on removing the dried piece 24 hours later yields a catenary curve (rather like the opening curvature of the helix generated by the golden mean below). This gives the sculpture great stability and natural spring, and like the Earth, it is, as a result, an oblate spheroid.
The globular gallery is designed with 37 steam bent ribs – a convenient opening at the front for people to step in to structure. I have always thought of it as John Ruskin’s Mind – ideas within leaking out, ideas without leaking in.
The design also allows disabled access as I have taken a bite out of the floor so that you can feel that you are right inside – even in a wheel chair, and sit comfortably too.
But why 37 ribs?
37 is a prime number in the Padovan sequence.
(a sequence of golden rectangles – Yin and Yang)
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