Solstice to solstice photo

[John Goodman]

"Six-month solargraphy - showing the sun’s high path in summer to low path in 
winter – taken over one of the sunniest cities in Canada."

http://earthsky.org/todays-image/suns-path-over-medicine-hat-alberta-canada
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Re: Golden Ratio and Sundials

[Fred Sawyer]

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.
Readers who have the (fantastic) NASS Repository. DVD can do an  easy
search to find the quiz.



On Jun 22, 2017 3:31 PM, "Donald L Snyder"  wrote:

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 apply to a sundial.  I see nothing obvious except these trivial
possibilities.  One could certainly construct a sundial on a rectangular
plate having a long side to short side ratio that is golden.  A
second possibility has the golden ratio pretty much hidden.  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 wrote:



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 ratio, then the
golden ratio is also called the golden section.

If the interval between two numbers is divided into two intervals related
by the golden ratio, then the golden ratio is also called the golden mean.



> For example if you look at a photograph of something where do you put the
> markers to make the measurement?
>

Along two mutually-perpendicular edges, measured from a common corner?  :^)


Michael Ossipoff



> Brooke 
> Clarkehttp://www.PRC68.comhttp://www.end2partygovernment.com/2012Issues.html
>
>  Original Message 
>
> 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
>
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>


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Re: Golden Ratio and Sundials

[Steve Lelievre]

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 wrote:
>
>
>
> 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 ratio, then
> the golden ratio is also called the golden section.
>
> If the interval between two numbers is divided into two intervals related
> by the golden ratio, then the golden ratio is also called the golden mean.
>
>
>
>> For example if you look at a photograph of something where do you put the
>> markers to make the measurement?
>>
>
> Along two mutually-perpendicular edges, measured from a common corner?  :^)
>
>
> Michael Ossipoff
>
>
>
>> Brooke 
>> Clarkehttp://www.PRC68.comhttp://www.end2partygovernment.com/2012Issues.html
>>
>>  Original Message 
>>
>> 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
>>
>>
>>
>> ---
>> https://lists.uni-koeln.de/mailman/listinfo/sundial
>>
>>
>>
>
>
> ---https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
> --
Cell +1 778 837 5771
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Re: Golden Ratio and Sundials

[Donald L Snyder]

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 apply to a sundial.  I see nothing obvious except these trivial
possibilities.  One could certainly construct a sundial on a rectangular
plate having a long side to short side ratio that is golden.  A
second possibility has the golden ratio pretty much hidden.  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 wrote:



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 ratio, 
then the golden ratio is also called the golden section.


If the interval between two numbers is divided into two intervals 
related by the golden ratio, then the golden ratio is also called the 
golden mean.


For example if you look at a photograph of something where do you
put the markers to make the measurement?


Along two mutually-perpendicular edges, measured from a common 
corner?  :^)



Michael Ossipoff

Brooke Clarke
http://www.PRC68.com
http://www.end2partygovernment.com/2012Issues.html


 Original Message 

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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