Tuesday 28 October 2014

Spiralling Inwards

Drawing One in the Nautilus set. Actually, Drawing Two, but it's the first one I have finished because it will set the size of the other three.

Nautilus Two - Construction, Megan Hitchens, 2014, black ink on tinted paper

I went and tinted another sheet of paper with yellow ochre (properly this time. Thanks to Mark Calderwood and Jo Abrahams), and cut it into sections. I need to tint one more sheet to have enough for the full set of four, and then I'll have leftovers for play.

Each piece is cut to the ratio of 2φ:2φ+1, same as the rectangles that build the spiral itself.

This was a bit of a challenge for me as I was working backwards. I can draw these in my sleep, providing I am working from a square outwards. But because I wanted the spiral placed precisely in the centre of the page, this time I had to work inwards. It took me a couple of tries to readjust, but once I came to grips with it the thing just sailed along. I really, really love Golden Spirals. All the construction lines are left in purposefully, and I have notations for the φ ratios at the side. Although looking at them now I think two of them are misplaced. They are correct, but would have been more helpful arranged a little differently.

All the construction lines are left in so that hopefully people can see how elements on the actual Nautilus shells, internal and external, relate to the geometry. The Nautilus is an amazing geometer. One of Nature's marvels.

So here's the question. I am thinking of putting ratio notation under the spiral, probably aligned with the left edge. Something like this:

0A = 1 
0B = φ 
0C =  φ 2 
0D = φ 3 
CD = φ 4

Should I do this or not? Would it be helpful or confusing or just pointless? I love how all these things relate to each other, but I know I am a bit weird, so I can't really see this one clearly. Suggestions?

(and, because I couldn't resist, despite the picture quality):

 

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