THE GOLDEN SECTION: 4 constructing a Golden Spiral

[@pTpArtRecordStudio]

Good to see you upload vods again =) Thanks alot

[@davidnicholls100]

Thanks Dag. I did these four years ago, uploaded them and then forgot to press the 'publish' button! What an idiot!

[@barbclark69]

I want to ask about your pet spider wandering across your page! Love the Golden Spiral. There’s a great book called The Power of Limits. I’m sure you know of it.

[@davidnicholls100]

Yes, I know the book. What was it you wanted to ask me about the spider? Thanks for your comment Barbara.

To be nitpicky, what is constructed here is not a Golden Spiral, but rather an approximation of one using quarter-circle arcs. It's a pretty decent approximation, depending on the interval sometimes it is even impossible to tell the difference with a naked eye. However, a true Golden Spiral has all higher derivatives as continuous functions (since the derivative of an exponential function is another exponential function), whereas a collection of circular arcs has discontinuities even in the second derivative. Again, this is quite nitpicky, as you're probably not going to get the necessary precision using a ruler and a compass to tell the difference.

[@davidnicholls100]

Yes, you're right, I appreciate that. I just didn't want to complicate matters! I'm not sure how I'd go about constructing a perfect golden spiral, and as you say it's virtually impossible to see the difference with the naked eye, and I'm only interested in the subject from an artistic point of view. Thanks for you comment Kresimir

[@larryrud8526]

Is that a pet spider?

[@davidnicholls100]

yes

[@deprimat666]

The Maori probably learnt from the celts

[@davidnicholls100]

probably

[@johngabana6328]

What's next the Celts inventing water?

[@deprimat666]

@@johngabana6328 celts are older than the Maori, my mums Maori and has Maori designs that look like this. That is why I said the Maori probably learnt off them