Where can I buy a Fibonacci Gauge??

[Tim Plantz]

Hello all,

Being an up and coming custom furniture builder, I've become increasingly impressed with the use of the Fibonacci Gauge. Since I don't have the time to build one, can anyone tell me where I might buy a good one??

Thanks in advance!

[Jason Whelehon]

I work at a woodcraft store and I know we have one on our shelves. I can't find it on the website.

[Jason Whelehon]

I think I found it. Is this what you're looking for?

http://www.woodcraft.com/family.aspx?FamilyID=3796

[Tim Plantz]

Thanks for the response Jason. The gauge I'm looking for is similar, that is, designed the same way, but offers a "Phi" or golden rule measurement instead of the equal distances which is what the one pictured provides.

[Jason Beam]

Can't say i've ever seen one for sale ... don't mean they ain't out there .... but ...

in the time you have spent here asking for or looking for one to buy, you probably coulda made one... just a few sticks of wood and a couple nuts/bolts/washers and you'd be done :)

[Chris Kennedy]

Tim,

It isn't a gauge, but Lee Valley has \phi rulers. They allow you to measure a true length and then either scale up or scale down by \phi:

http://www.leevalley.com/wood/page.aspx?c=2&p=57625&cat=1,43513

Also, you can use successive Fibonacci numbers to approximate \phi very well.

Hope that helps,

Cheers,

Chris

[Roger Savatteri]

Hello all,

Being an up and coming custom furniture builder, I've become increasingly impressed with the use of the Fibonacci Gauge. Since I don't have the time to build one, can anyone tell me where I might buy a good one??



For an in-depth exploration of the Golden Mean, take a look at ... http://www.youtube.com/watch?v=2zWivbG0RIo


Here's a youtube quick explanation and a how to video ......http://www.youtube.com/watch?v=5Xgw84Kwrh8



as to a several manufactured versions, try this..... http://www.goldenmeangauge.co.uk/catalog/index.php?cPath=0_1


R.

[Chris Kennedy]

For an in-depth exploration of the Golden Mean, take a look at ... http://www.youtube.com/watch?v=2zWivbG0RIo



That video was . . . interesting. I particularly liked the bit about the "mysterious reason" that the Fibonacci numbers appear in nature. Maybe they should interview a PhD who isn't from an Economics institute. I have my doubt that he has much mathematical education.

There isn't any mystery about it. It all follows from the idea of self-similarity. Object A is similar to object B if one is a scaled version of the other (think similar triangles from high school geometry -- they have the same angles, and consequently have the same proportions, even if they are different sizes).

Many things in nature exhibit self-similarity. As they grow, they maintain the same proportions, even as they grow larger. This is true in low-level organisms and complex organisms (even humans).

To find the Golden ratio, fix a set unit length, 1. Then we want a number x such that when it is increased by one, it remains similar to itself. Hence, the fractions x/1 and (x+1)/x must be equal. Clear denominators and x^2 = x+1. Apply the quadratic formula, and x=\frac{1+\sqrt{5}}{2} (the other root is negative, which rules it out since we are looking for a length).

Alright, now notice that x^2 = x+1 is a lot like the formula for generating Fibonacci numbers: F_{n+1} = F_n + F_{n-1}. This isn't coincidental. Use a little algebra, and we can derive Binet's formula: F_n = \frac{1}{\sqrt{5}}(\phi^n - (1-\phi)^n. The upshot: Fibonacci numbers are intrinsically related to self-similarity. Moreover, the starting point for the Fibonacci numbers (1 and 1) mean that if we are starting with a set unit length, ratios of Fibonacci numbers are going to be close to \phi.

Fibonacci numbers are whole numbers whose ratios are close to \phi. Hence, any organism that grows in discrete amounts (sunflower seeds, nautilus shells) that starts with a single unit and tends to look like itself as it grows, will likely follow the Fibonacci numbers.

And thus, that is why you can use Fibonacci numbers to get a very good approximation of the Golden ratio.

And it is also why we like the Golden mean -- simply because as things grow, they maintain the same proportions. It is what we are used to.

Cheers,

Chris

[Mark Hulette]

Hello all,

Being an up and coming custom furniture builder, I've become increasingly impressed with the use of the Fibonacci Gauge. Since I don't have the time to build one, can anyone tell me where I might buy a good one??

Thanks in advance!

There was a simple plan in Woodmagazine a while back showing how to make one just in case you can't buy one.

[glenn bradley]

Here you go: http://woodstore.woodmall.com/figaandhowto.html

[Larry James]

Check this thread
http://sawmillcreek.org/showthread.php?t=66031&highlight=golden+ratio...and,

you will find...
http://goldennumber.net/gauges.htm...and,

you will also find a plan, with dimensions, by Joe Greiner.

A tread on SMC recommend the book:The Golden Ratio, by Mario Livio.

I ordered the book from Amazon - a paperback - and I think the book cost less than $10. If you are into math and history you may want to read it.

Coincidentally, my skp avatar kinda looks like Fig. 40, on page 119 of the book.

Larry

[Brandon Shew]

Why not just use a calculator? Multiply your reference distance by 1.618.

[Larry James]

Why not just use a calculator? Multiply your reference distance by 1.618.

That would work, but it's not a TOOL.;)

[Frank Drew]

The Parthenon notwithstanding, I actually don't think that the Golden Mean (if defined as 1:1.6...) necessarily provides the best (most pleasing) proportions for any particular piece of furniture.

[Larry James]

The Parthenon notwithstanding, I actually don't think that the Golden Mean (if defined as 1:1.6...) necessarily provides the best (most pleasing) proportions for any particular piece of furniture.

Good point. The Golden Mean by itself is not the only design solution, but one of many ways - including form follows function - to achieve the best proportions. As always, common sense has a part to play.

That said, the Golden Mean is still a "beautiful" number.

Larry

[Steve Schoene]

Maybe they should interview a PhD who isn't from an Economics institute. I have my doubt that he has much mathematical education. Chris

Economics is a pretty mathematical discipline, so I did a quick google on Dr. Casti. He has his Ph.D. in mathematics from USC. Check out his biography. http://www.anova.org/bio/casti.html

[Glenn Clabo]

How about his pubs...this is one interesting dude.
http://www.amazon.com/exec/obidos/search-handle-url?%5Fencoding=UTF8&search-type=ss&index=books&field-author=John%20L.%20Casti

[Chris Kennedy]

I stand both corrected and chastened. Serves me right for not doing a literature search before opening my mouth.

I looked him up on MathSciNet, and he has an impressive number of publications (97). Mostly in more applied areas of mathematics, but I assume he has seen Binet's formula which relates \phi and the Fibonacci numbers explicitly

Honestly, though, I am still puzzled by his comment about it being "mysterious." Admittedly when you first see the Fibonacci sequence in nature, it seems really strange, especially when you see it in disparate places. On the other hand, once you realize its connection to \phi and self-similarity, it's pretty clear why it should happen. And the math underlying it really isn't hard. We teach this in one of our freshman "Math for Liberal Arts" courses.

Maybe it just doesn't make for interesting YouTube. I don't know.

A chastened and humbled,

Chris

[mike roe]

That proportion is deemed mysterious not because of how it works but because where you find it. check this out - http://goldennumber.net/life.htm

[Ted Jay]

Hello all,

Being an up and coming custom furniture builder, I've become increasingly impressed with the use of the Fibonacci Gauge. Since I don't have the time to build one, can anyone tell me where I might buy a good one??

Thanks in advance!

It's kinda pricey, but you can buy one from across the pond, stainless steel to boot.

http://www.goldenmeangauge.co.uk/trolleyed/2/index.htm

http://naturalpigments.com/detail.asp?PRODUCT_ID=655-GMSTD


Ted

[Andy Richards]

You guys seen the movie "Pi (http://www.imdb.com/title/tt0138704/)", by Darren Aronofsky? It's about a guy going crazy looking for a number like this.

[Larry James]

You guys seen the movie "Pi (http://www.imdb.com/title/tt0138704/)", by Darren Aronofsky? It's about a guy going crazy looking for a number like this.
No, but I think the movie "A Beautiful Mind" (http://www.imdb.com/title/tt0268978/) had a similar theme.

Larry