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Golden Ratio Dividers



 
 
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  #1  
Old June 16th 07, 06:58 AM posted to alt.binaries.pictures.woodworking
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Posts: 2,387
Default 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/




Attached Thumbnails
Golden Ratio Dividers-gr_divider-jpg  
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  #2  
Old June 16th 07, 07:19 PM posted to alt.binaries.pictures.woodworking
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Posts: 6,380
Default 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.
Attached Thumbnails
Golden Ratio Dividers-%5Ctriangles-jpg  
  #3  
Old June 16th 07, 07:40 PM posted to alt.binaries.pictures.woodworking
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Posts: 2,387
Default 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  
Old June 16th 07, 09:59 PM posted to alt.binaries.pictures.woodworking
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Posts: 6,380
Default 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  
Old June 16th 07, 11:31 PM posted to alt.binaries.pictures.woodworking
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Posts: 2,387
Default 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 how-to-build 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  
Old June 16th 07, 11:37 PM posted to alt.binaries.pictures.woodworking
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Posts: 118
Default 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  
Old June 17th 07, 04:38 AM posted to alt.binaries.pictures.woodworking
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Posts: 6,037
Default Golden Ratio Dividers

Careful Morris, this argument will easily slip into a loop before you know
it.


  #8  
Old June 17th 07, 06:21 AM posted to alt.binaries.pictures.woodworking
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Posts: 2,387
Default 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
arbitrary-length 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/




Attached Thumbnails
Golden Ratio Dividers-gr_baseline-jpg  
  #9  
Old June 17th 07, 05:58 PM posted to alt.binaries.pictures.woodworking
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Posts: 6,380
Default 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
arbitrary-length 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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