uot;
> Cc: "Michael Ossipoff" , "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 t
may want to purchase the series of books. Of course they
will not $2.
Regards,
Roderick Wall.
- Reply message -
From: "Frank King"
To: "Geoff Thurston"
Cc: "Michael Ossipoff" , "Sundial Mailing List"
Subject: Golden Ratio and Sundials
Date: Sat,
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
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 s
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 Vegas
Hi All
This is the golden ratio Sundial
https://www.youtube.com/watch?v=WA-WwWGUCA8&feature=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 ever
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 t
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 there is a
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"
To: "'rodwall1...@gmail.com'" ,
Subject: Golden Ratio and Sundials
Date: Sat, Jun 24, 2017 2:34 AM
Rod:
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
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.
R
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, Michael Ossipoff wr
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 ap
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 parts related by that ra
Hi Brooke,
Thanks, I can see that your information is from Da Book.
Roderick.
- Reply message -
From: "Brooke Clarke"
To: "'Sundial Mailing List'"
Subject: Golden Ratio and Sundials
Date: Thu, Jun 22, 2017 7:27 AM
Hi Roderick:
I also have a book on t
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 camera
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 Gol
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