Fibonacci Dividers

[Michael Ray Smith]

I had never heard of Fibonacci or Golden Ratio dividers (or calipers) until Jim Koepke posted this a while back: http://www.sawmillcreek.org/showthread.php?223546-What-s-in-a-Name&p=2330822#post2330822

Here's a set I made from a piece of 1/4" x 1 1/2" black walnut stock that I had. The hinges are just pins cut from 1/4" dowel with the ends glued to the circles, which are whittled from the same stock. I found the dimenions on several web sites. The two outside legs are 340 mm from pin to tip, and the middle one is 210 mm from pin to tip. The distance between each pair of pins is 130 mm. I didn't give much thought to constructing it. I marked and drilled the holes before I cut the pieces out of one piece of stock. It didn't occur to me until later that I should have cut the pieces first, stacked them, and drilled the holes through all four of them at the same time. Two holes to drill instead of eight, and it would have insured all the pins to be equidistant. I just whittled the tips freehand. A little more care to make sure the tips are colinear with the pins would have made the dividers a bit more accurate. But accuracy didn't matter much to me, given that I have no earthly idea what I might use them for anyway. I just think they're sorta cool.

306722

[Michael Ray Smith]

More about the golden ratio. http://en.wikipedia.org/wiki/Golden_ratio

[Jim Koepke]

Great looking work Ray.


I didn't give much thought to constructing it. I marked and drilled the holes before I cut the pieces out of one piece of stock. It didn't occur to me until later that I should have cut the pieces first, stacked them, and drilled the holes through all four of them at the same time. Two holes to drill instead of eight, and it would have insured all the pins to be equidistant.

My plans are to eventually build a few more pairs of these. One thought is to drill the holes and then rip the pieces from one piece of stock before cutting to length.

jtk

[Patrick Harper]

Those are very cool. I purchased this book a long time ago and it talks a lot about the golden ratio, and geometry in general. It even has several exercises. http://www.amazon.com/Sacred-Geometry-Philosophy-Practice-Imagination/dp/0500810303/ref=sr_1_3?s=books&ie=UTF8&qid=1423744036&sr=1-3&keywords=sacred+geometry

Also, you should definitely check out "By Hand and Eye" if you haven't already. I think design and aesthetics are the two things most often ignored in the woodworking community.

[Michael Ray Smith]

One thought is to drill the holes and then rip the pieces from one piece of stock before cutting to length.

jtk

A cat that can be skinned in more ways than one, as long as the holes in each legs are pretty close to the same distance apart. If one pair of holes is a bit off, the rhombus in the middle of the dividers will turn into a trapezoid, and the dividers will bind. At least I think that's what will happen.

[David Ragan]

Yes, the 1:1.67 ratio, The Golden Ratio, is something I start out with in all my stuff.

LN has a DVD "unlocking the secrets of traditional design" that explains a lot of simple stuff that is important about designing furniture/display cabinets, etc.

[James Conrad]

Yes, the 1:1.67 ratio, The Golden Ratio, is something I start out with in all my stuff.

LN has a DVD "unlocking the secrets of traditional design" that explains a lot of simple stuff that is important about designing furniture/display cabinets, etc.

Since you mentioned George Walker's DVD you may find this interesting: https://georgewalkerdesign.wordpress.com/2010/01/29/golden-rectangle-a-different-viewpoint/

[Michael Ray Smith]

Yes, the 1:1.67 ratio, The Golden Ratio, is something I start out with in all my stuff.

Yeah, that's where the aesthetics and the math diverge a bit. The mathematical golden ratio is an irrational number, 1.61803398875..., according to Mr. Google. For aesthetics purposes, one and two-thirds is close enough.

[Don Orr]

Yes, the 1:1.67 ratio, The Golden Ratio, is something I start out with in all my stuff.


Be careful-the actual ratio is 1:1.618 not 1.67. Probably just a typo.

[Pat Barry]

But accuracy didn't matter much to me, given that I have no earthly idea what I might use them for anyway. .

306722

Yes, I think we should see what this thing can be used for exactly. Have you tried using it to establish various rectangles for example? Maybe some nested rectangles with a common vertex? Like below with 4 nested golden sections (acording to sketchup)
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[Jim Koepke]

Yes, I think we should see what this thing can be used for exactly. Have you tried using it to establish various rectangles for example?

Mine was used to determine the outside dimensions of a tea cabinet built for my wife.

http://www.sawmillcreek.org/showthread.php?224747-Tea-Cabinet-Latest-Project

jtk

[David Ragan]

Be careful-the actual ratio is 1:1.618 not 1.67. Probably just a typo.

Too funny! I haven't had a laugh out loud in a while. Too serious up here in my head.

Several years ago, they had the book "Dont Sweat the Small Stuff". Good.

Then they put out a workbook for same. Wow.

[Jim Koepke]

Since you mentioned George Walker's DVD you may find this interesting: https://georgewalkerdesign.wordpress.com/2010/01/29/golden-rectangle-a-different-viewpoint/

An interesting read. He mentions ratios of 3:5 and 5:8. Those are ratios in the Fibonacci sequence. (1,1,2,3,5,8,13... )

3:5 = 1.667
5:8 = 1.6

Not an exact match to the "golden mean," but somewhat close.

There is a point in design where something will look too squat, too thin or just right. For some reason to most human eyes, the ratio of these relationships falls roughly in the neighborhood of the Fibonacci sequence.

jtk

[Michael Ray Smith]

An interesting read. He mentions ratios of 3:5 and 5:8. Those are ratios in the Fibonacci sequence. (1,1,2,3,5,8,13... )

3:5 = 1.667
5:8 = 1.6

Not an exact match to the "golden mean," but somewhat close.

There is a point in design where something will look too squat, too thin or just right. For some reason to most human eyes, the ratio of these relationships falls roughly in the neighborhood of the Fibonacci sequence.

jtk

Astute observation, Jim. As you keep extending the Fibonacci series, the ratio of one number in the sequence divided by the previous number approaches the golden ratio. As you show above, one ratio is above the golden mean, and the next ratio is below. Extended to infinity, the ratio converges on the golden mean.

BTW, ever notice that credit cards are very close to golden rectangles?

[Andrew Kertesz]

I thought credit cards were made that size so we didn't need bigger wallets.....:D

[James Conrad]

I agree with Walker's assessment that preindustrial revolution furniture was designed with proportions in consideration and not golden ratios. For artists, designers of furniture, those interested in the visual - there is no need to know golden ratios or for that matter proportions based on greek columns. Those concerned with making art, and I do consider furniture making an art, have an innate ability to see which informs their work and create free of such constraints.

For industrial and commercial designers these things are useful, but not for someone who's greatest struggles are to create and grow. I think EE Cummings said something close to the later part of that.

I do find Fibonacci and golden ratios interesting, but in terms of furniture design I don't worry about it.