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, Tulsa, Gibraltar.... Gardner notes this is "an isosceles
triangle that has sides in golden ratio to its base" (p. 71).
best wishes,
Peter
On 24/06/2017 10:48, Fred Sawyer wrote:
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 the Style’s height [are] all equal.
The problem originated with Edward Hauxley in a challenge issued to
Charles Leadbetter Feb. 1, 1736/7. Leadbetter struggled with the
solution, developing a 4th degree polynomial whose solution gave him a
value for the declination. He then fit this value into other
equations to come up with a slightly different value for the latitude.
The correct solution is that the latitude is 38d 10m 22s and that this
is also the value of the other angles sought. The solution involves
finding that the sine of the required latitude is the reciprocal of
the golden ratio.
To see the article, download it at:
https://www.dropbox.com/s/bj2qk6s1hg3a5m2/Pages%20from%20Nass43.pdf?dl=0
Fred Sawyer
On Wed, Jun 21, 2017 at 5:04 PM, rodwall1...@gmail.com
<rodwall1...@gmail.com <mailto:rodwall1...@gmail.com>> wrote:
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
Golden Ratio. The Golden Ratio goes back in history so one wonders
if it was ever applied to sundials.
The book describes that the short and long sizes of credit cards
are close to being the Golden Ratio.
LongSide/ShortSide = Golden Ratio.
Regards,
Roderick Wall.
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Peter Mayer
Department of Politics & International Studies (POLIS)
School of Social Sciences
http://www.arts.adelaide.edu.au/polis/
The University of Adelaide, AUSTRALIA 5005
Ph : +61 8 8313 5609
Fax : +61 8 8313 3443
e-mail: peter.ma...@adelaide.edu.au
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