I’ve been reading this book, The Golden Section.
Maybe this is a lie, as, after three days I’m still only on page two.
My notebook is full of cross-outs. Each time I think I finally understand what’s going on I write bigger. The pages of my notebook looks like a map to insanity. Maybe a bit of insanity is what it takes, so I can finally disconnect from what’s already in my head.
I have to let go of preconceptions before I can finally see, sitting so smugly, so adorable but nearly invisible, right in front of me, the detail I’ve overlooked. (Got to be good lookin’ ‘cuz he’s so hard to see….)
This is a scaling issue. As someone who is interested in paper-folding and book making I am always scaling things. Thought I completely understood scaling. Scaling helps me do things I want to do nearly every day. But there is the wall (or ceiling?) I keep bumping up against. Am trying to work it out, from many fronts. Last few days, trying to understand the golden ratio, is one of the many ways that I am trying to deepen my understanding of scale. Also, there’s something about pentagons that I just don’t get. I don’t know what it is about pentagons that is eluding me, but I know golden ratio and regular pentagons are two peas in a pod (sorry, not a good metaphor. I think I’m hungry).
We’ve all seen the golden ratio spiral, embedded in a rectangle which contains successively smaller squares created in the leftover part of the rectangle once the biggest square is made. My mind doesn’t think in spirals, though, so I can’t extrapolate that image into something that I can get cozy with.
I love number lines, but I’ve had a heck of a time seeing the golden ratio on a number line. Over and over I have read description of a line divided to show the golden ratio, and, although I understand what it’s saying, the words never make the image snap into focus. What I want is an aha! moment, an image I can conjure up effortlessly and know what I am seeing.
Finally opened my favorite graphic program. Started making circles. Took a few minutes but, oh, yeah, AHA!. Maybe I am the only person that this makes sense to but that’s okay. At least it makes sense to me.
This is a two-step visual. It doesn’t prove anything. It’s just a way for me to visualize what’s going on.
The circles above are enlarged by the same proportion over and over again. They aren’t increasing by twice their size, which would be 200%. They are increasing by 161.8%. And using this specific percentage, makes something happen that seems unlikely….
What happens is that the two smaller circles fit exactly into the next larger circle.
Now this is an image I can conjure up and understand.
And play with. Hmm.
Needs to show all the circles fitting into other circles
Needs to see what other arrangements work.
But, even more pressing, I need to get to sleep. So no more color tonight.
Tomorrow I will be ready for page 3.
After getting some rest, made this. Lots of golden ration circles.