Re: Golden Ratio and Sundials

[Peter Mayer]

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 
> 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
CRICOS Provider Number 00123M
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ODP: Golden Ratio and Sundials

[Marek Szymocha]

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 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 spiral 
sundial. Where a spot of light marked 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:

 

Do a goggle image search on “spiral clock face”.  A similar sundial face design 
could be made.   Time marks and numerals could be adjusted to be in the proper 
positions to be a functional sundial.

 

 

 

From: sundial [mailto:sundial-boun...@uni-koeln.de] On Behalf Of 
rodwall1...@gmail.com
Sent: Wednesday, June 21, 2017 2:04 PM
To: sundial@uni-koeln.de
Subject: 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 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.

 


---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Golden Ratio and Sundials

[Fred Sawyer]

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> 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.
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
---
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RE: Golden Ratio and Sundials

[John Carmichael]

Rod:

 

Here are photos of actual clocks for sale with spiral faces.  Notice that the 
hour numerals in each turn of the spiral are radially aligned so that the clock 
hands point to the same numerals in all the turns.  A planar equatorial dial 
would be the perfect dial type to use in this design.  See : 
http://www.cafepress.com/+spiral+clocks   The dial you referred to was invented 
by Bill Gottesman and it takes the form of a 3D helix.

 

regards

 

From: rodwall1...@gmail.com [mailto:rodwall1...@gmail.com] 
Sent: Friday, June 23, 2017 2:36 PM
To: John Carmichael; sundial@uni-koeln.de
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 spiral 
sundial. Where a spot of light marked 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:
 
 
 
Do a goggle image search on “spiral clock face”.  A similar sundial face design 
could be made.   Time marks and numerals could be adjusted to be in the proper 
positions to be a functional sundial.
 
 
 
 
 
 
 
From: sundial [mailto:sundial-boun...@uni-koeln.de] On Behalf Of 
rodwall1...@gmail.com
Sent: Wednesday, June 21, 2017 2:04 PM
To: sundial@uni-koeln.de
Subject: 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 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.
 
 
 
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Golden Ratio and Sundials

[rodwall1...@gmail.com]

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 spiral 
sundial. Where a spot of light marked 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:



Do a goggle image search on “spiral clock face”.  A similar sundial face design 
could be made.   Time marks and numerals could be adjusted to be in the proper 
positions to be a functional sundial.







From: sundial [mailto:sundial-boun...@uni-koeln.de] On Behalf Of 
rodwall1...@gmail.com
Sent: Wednesday, June 21, 2017 2:04 PM
To: sundial@uni-koeln.de
Subject: 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 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.---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Gianni Ferrari

[Fred Sawyer]

The Minor Planet Center at the Smithsonian Astrophysical Observatory has
named asteroid n. 315046 after amateur astronomer and sundialist Gianni
Ferrari.


*Gianni Ferrari (b. 1938) is the founder of the Modena Amateur Astronomers
Group. He has given many lectures and written several articles and computer
programs and also two books about sundials calculation*


Gianni was informed that one of the factors leading to the decision was his
receiving the Sawyer Dialing Prize from NASS a couple years ago.


For more info, see  https://ssd.jpl.nasa.gov/sbdb.cgi  Enter as Name
315046  or   “Gianniferrari” .

With the "Orbit Diagram" option you can see the orbit
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Re: Golden Ratio and Sundials

[Frank King]

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/dodecahedral-sundial.ht
ml

The faces are all regular pentagons and the ratio of
the distance between any two non-adjacent vertices
and the length of a side is the golden ratio.

Exercise for the reader:

  Come up with a simple proof of this!

In some (slightly contrived) sense, a regular
pentagon incorporates 25 instances of the
Golden Ratio, so a Dodecahedron incorporates 300
such instances.

Frank H. King
Cambridge, U.K.

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