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#1




Golden Ratio Dividers
This allows anyone to build a golden ratio divider of any size at all.
The method is independent of measurement units (inches, mm, cubits, ad nausea). The attached drawing shows the design layout. Note that all angles are either 90 or 45 degrees (It's pretty obvious which are which). Wherever two lines meet, there's a pivot. Decide on the longest measurement you want the dividers to handle. Let's call it L. Either multiply L by 0.618 or divide it by 1.618. The result will be the span between the left point and the "middle" point. Let's call that Dmajor. Then the span between the "middle" point and the right point will be Sminor = L  Smajor. The only other piece of information needed is that the length of a side of a square is (roughly) 0.707 times the length of a diagonal. One of the things that ocurred to me as I made the drawing was that there's no limit to the number of "middle" arms this thing can have, and that even with just one arm, you can set up any ratio you want (eg: divide any span into thirds).  Morris Dovey DeSoto Solar DeSoto, Iowa USA http://www.iedu.com/DeSoto/ 
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#2




Golden Ratio Dividers  \triangles.jpg [01/01]
In article , "Morris Dovey" wrote:
This allows anyone to build a golden ratio divider of any size at all. The method is independent of measurement units (inches, mm, cubits, ad nausea). Sorry, Morris, but I don't agree. Consider the attached  the ratio is not fixed at 1:0.618, but instead depends on how far the diagonals (indicated in red) are produced from the square.  Regards, Doug Miller (alphageek at milmac dot com) It's time to throw all their damned tea in the harbor again. 
#3




Golden Ratio Dividers  \triangles.jpg [01/01]
Doug Miller wrote:
 In article , "Morris  Dovey" wrote:  This allows anyone to build a golden ratio divider of any size at  all. The method is independent of measurement units (inches, mm,  cubits, ad nausea).   Sorry, Morris, but I don't agree. Consider the attached  the  ratio is not  fixed at 1:0.618, but instead depends on how far the diagonals  (indicated in  red) are produced from the square. Thank you for agreeing with my point that the dividers can be produced for any ratio. :) Possibly you didn't notice that the ratio was the starting point for, rather than the consequential result of, the construction approach...  Morris Dovey DeSoto Solar DeSoto, Iowa USA http://www.iedu.com/DeSoto/ 
#4




Golden Ratio Dividers  \triangles.jpg [01/01]
In article , "Morris Dovey" wrote:
Possibly you didn't notice that the ratio was the starting point for, rather than the consequential result of, the construction approach... That being the case, I confess I don't see its utility  since you have to have segments that are already in the golden ratio in order to construct the dividers.  Regards, Doug Miller (alphageek at milmac dot com) It's time to throw all their damned tea in the harbor again. 
#5




Golden Ratio Dividers
Doug Miller wrote:
 That being the case, I confess I don't see its utility  since you  have to  have segments that are already in the golden ratio in order to  construct the  dividers. Now you've lost me. Are you looking for a way to build the tool without using any measurements at all? If so, you can DAGS and find a number of ways to get there with a compass and straightedge. What I've provided is a method for calculating all of the measurements needed to build the tool from the numerical value of the ratio and the length of the longest workpiece edge with which the tool will be used. The _tool_ has no utility at all for my woodworking  since all I need to do is incorporate the ratio into a CNC part program  but Scott (over on the wRec) was looking for a howtobuild article. I'm sure he'd be interested (as am I!) in your method.  Morris Dovey DeSoto Solar DeSoto, Iowa USA http://www.iedu.com/DeSoto/ 
#6




Golden Ratio Dividers  \triangles.jpg [01/01]
Doug Miller wrote:
In article , "Morris Dovey" wrote: This allows anyone to build a golden ratio divider of any size at all. The method is independent of measurement units (inches, mm, cubits, ad nausea). Sorry, Morris, but I don't agree. Consider the attached  the ratio is not fixed at 1:0.618, but instead depends on how far the diagonals (indicated in red) are produced from the square. But, once the dividers are constructed of a length to give the fixed ratio, will the ratio remain the same when the dividers are opened or closed? That will be the important point.  Gerald Ross Cochran, GA The early worm gets the bird. 
#7




Golden Ratio Dividers
Careful Morris, this argument will easily slip into a loop before you know
it. 
#8




Golden Ratio Dividers
Leon wrote:
 Careful Morris, this argument will easily slip into a loop before  you know it. LOL  Nope, Doug is just acting like a geometer. I've attached a pair of drawings that allow using a straightedge and compass to first construct a pair of properly proportioned line segments in the golden ratio and, second, to use those lengths to construct an arbitrarylength baseline. No measuring scale/rule/ruler required. Once the base line has been established, I trust Doug won't have any difficulty constructing the legs shown in the previous drawing. :) Legend: Red lines show compass work; blue lines show straightedge work. I probably needed the exercise. ;)  Morris Dovey DeSoto Solar DeSoto, Iowa USA http://www.iedu.com/DeSoto/ 
#9




Golden Ratio Dividers
In article , "Morris Dovey" wrote:
Leon wrote:  Careful Morris, this argument will easily slip into a loop before  you know it. LOL  Nope, Doug is just acting like a geometer. I've attached a pair of drawings that allow using a straightedge and compass to first construct a pair of properly proportioned line segments in the golden ratio and, second, to use those lengths to construct an arbitrarylength baseline. No measuring scale/rule/ruler required. Simple and elegant. Thanks, Morris. Once the base line has been established, I trust Doug won't have any difficulty constructing the legs shown in the previous drawing. :) No indeed.  Regards, Doug Miller (alphageek at milmac dot com) It's time to throw all their damned tea in the harbor again. 
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