Re: Golden Ratio and Sundials

2017-06-24 Thread Geoff Thurston
Rod, Thanks for the information. They look as if they have been been attractively produced but in the UK, Issue 1 is available at £1.99 while Issue 3 onwards costs £8.99. So I shall not be subscribing £450 for a complete set even if I had room on my shelves. Best wishes, Geoff On 24 June 2017

Re: Golden Ratio and Sundials

2017-06-24 Thread rodwall1...@gmail.com
Hi Geoff and Frank, My book also shows this. By The Way, the book is one of a series called the Mathematical World by National Geographic. Where in Australia the 1st book. The Golden Ratio. The mathematical language of beauty. Was AUD $2. $2 to get you to purchase the 1st book. And then you may

Re: Golden Ratio and Sundials

2017-06-24 Thread Frank King
Dear Geoff, Many congratulations on your proof... When I set the puzzle, I thought three things: 1. I am really setting this for Geoff to solve. 2. He will certainly solve it and will probably be the first to publish. 3. His proof will either match mine or be more elegant. I was ri

Re: Golden Ratio and Sundials

2017-06-24 Thread Geoff Thurston
Frank, I think the most elegant proof that the diagonal to side ratio in a pentagon equals phi is as shown in the attachment. Geoff On 23 June 2017 at 08:08, Frank King wrote: > Dear All, > > Referring to the Golden Ratio and Sundials, Donald > Snyder wrote: > > I see nothing obvious excep