Re: Golden Ratio and Sundials

@cl.cam.ac.uk> > To: "Geoff Thurston" <thurs...@hornbeams.com> > Cc: "Michael Ossipoff" <email9648...@gmail.com>, "Sundial Mailing List" < > sundial@uni-koeln.de> > Subject: Golden Ratio and Sundials > Date: Sat, Jun 24, 2017 8:1

Re: Golden Ratio and Sundials

il.com>, "Sundial Mailing List" <sundial@uni-koeln.de> Subject: Golden Ratio and Sundials Date: Sat, Jun 24, 2017 8:16 PM 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 certa

Re: Golden Ratio and Sundials

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

Re: Golden Ratio and Sundials

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 <f...@cl.cam.ac.uk> wrote: > Dear All, > > Referring to the Golden Ratio and Sundials, Donald > Snyder

Re: Golden Ratio and Sundials

Hi, Further to Fred's puzzle solution, here's an illustration from Martin Gardner's /More Mathematical Puzzles and Diversions/ (Harmondsworth: Penguin Books, Ltd., 1961) p. 74. The base angles are 72 degrees, the apex 36 degrees, so a suitable gnomon for Abany in Western Australia, Las

ODP: Golden Ratio and Sundials

Hi All This is the golden ratio Sundial https://www.youtube.com/watch?v=WA-WwWGUCA8=youtu.be Best Regards Marek Od: rodwall1...@gmail.com Wysłano: piątek, 23 czerwca 2017 23:36 Do: John Carmichael; sundial@uni-koeln.de Temat: Re: Golden Ratio and Sundials Hi all and thanks to everyone who

Re: Golden Ratio and Sundials

In 1997, I presented the following problem in The Compendium: Problem: It is required to know in what Latitude of this terraqueous Globe, an Erect South Declining Dial might be fixed to have these Properties, viz. the Declination of the Plane, the Distance of the Substyle from the Meridian, and

RE: Golden Ratio and Sundials

Subject: Re: Golden Ratio and Sundials Hi all and thanks to everyone who responded to my questions. All very interesting. John I have never see a spiral clock face. Very interesting thanks. Learn something every day. That had me thinking. I think I have seen somewhere where

Re: Golden Ratio and Sundials

the time on the numbers on the spiral. Wonder if it was a Golden Ratio spiral. Have fun, Roderick Wall. - Reply message - From: "John Carmichael" <jlcarmich...@comcast.net> To: "'rodwall1...@gmail.com'" <rodwall1...@gmail.com>, <sundial@uni-koeln.de> S

Re: Golden Ratio and Sundials

Dear All, Referring to the Golden Ratio and Sundials, Donald Snyder wrote: I see nothing obvious except ... trivial possibilities. Try Googling Dodecahedral Sundial and you will see many examples. Here is one chosen at random: http://stretchingtheboundaries.blogspot.co.uk/2012/09

Re: Golden Ratio and Sundials

Traveling now so I don't have access to it at the moment, but several years ago I published a quiz in The Compendium that had the golden ratio as the answer. It's was an actual historical example and the author back in the 17th? Century wasn't aware that the number he was approximating was phi.

Re: Golden Ratio and Sundials

On Thu, Jun 22, 2017 at 12:31, Donald L Snyder wrote: > Since > atan(1.61803) equals 58.28 degrees, a horizontal sundial in a city at > this latitude could have a triangular gnomon with a height to base > ratio that is golden. >Don Snyder > > On 6/21/2017 10:00 PM,

Re: Golden Ratio and Sundials

Thanks, Michael, for setting that right. I would add only that the golden ratio equals (sqroot(5) + 1)/2, which is a number approximately equal to 1.61803. The inverse of the golden ratio is approximately 0.61803. The original question posted by Roderick asked if the golden ratio could ever

Re: Golden Ratio and Sundials

On Wed, Jun 21, 2017 at 5:27 PM, Brooke Clarke wrote: > Hi Roderick: > > I also have a book on this number that makes the case that there is no > such ratio. > Your book is mistaken. If A/B = (A+B)/A, then A/B is the golden ratio. If a line-segment is divided into two

Re: Golden Ratio and Sundials

Hi Brooke, Thanks, I can see that your information is from Da Book. Roderick. - Reply message - From: "Brooke Clarke" <bro...@pacific.net> To: "'Sundial Mailing List'" <sundial@uni-koeln.de> Subject: Golden Ratio and Sundials Date: Thu, Jun 22, 2017 7:

Re: Golden Ratio and Sundials

Hi Roderick: I also have a book on this number that makes the case that there is no such ratio. For example if you look at a photograph of something where do you put the markers to make the measurement? It's interesting that 4x5, 8x10 film cameras have aspect ratios of 1.25. 35mm film

Golden Ratio and Sundials

Hi all, I have been reading a book on the Golden Ratio which is 1.6180339887. It describes how the Golden Ratio describes how the spiral of a sea shell is produced. And how nature uses the Golden Ratio on the size of leaves etc. Does anyone know if sundials have ever been produced useing the