Golden Ratio

[Dave Brandt]

For the life of me, I can't remember how to figure out the "golden ratio." Can someone please give me a quick slap upside the head and an EASY way to figure out how to make a box that is pleasing to the eye? db

[Dave Arbuckle]

Ratio is 1.618 : 1, close enough. Close enough because it actually is an irrational number.

Whether it is most pleasing or not is debatable.

Dave

[Dave Brandt]

Thanks Dave. I knew it was something simple, just can't remember stuff anymore (since I retired in January - stealth gloat!).

[Anthony Yakonick]

Check the size of your credit card.

[Pete Lamberty]

Hi Dave, The golden ratio or rectangle is one of the set of numbers that Fibonochi (spelling?) discovered/noticed. There are a number of them, not just the one that was mentioned here. They come from, I guess, just about all natural things. I guess that is why so many things in nature look beautiful to us. Look up Fibonochi numbers on the net or at the library. Then play with the different ratios when you design something. These should give you the best "look". Hope this helps. Pete

[Dave Arbuckle]

Fibonacci. It will help in an internet search.

The "golden ratio" was heavily, even slavishly, used by the ancient Greeks. Definitely not original to Fibonacci. It is hard to compare two of anthing in the Parthenon without finding that ratio.

Dave

[Dave Anderson]

Originally posted by Dave Arbuckle
Fibonacci. It will help in an internet search.

The "golden ratio" was heavily, even slavishly, used by the ancient Greeks. Definitely not original to Fibonacci. It is hard to compare two of anthing in the Parthenon without finding that ratio.

Dave

Dave, you never cease to amaze me! You are a living, breathing encyclopedia.

[Jason Roehl]

Here's how you figure it (from a former ex-math teacher neighbor of mine):

The ratio of the end of the rectangle to the side of the rectangle is the same as the ratio of the side to the sum of the end and the side.

So, if you have a rectangle of end length 1 and side x, the ratio is:

1/x = x/(x + 1)

If you go thru all the math, wave a magic wand, recite some ancient Gregorian chants, and apply the QUADRATIC FORMULA, you end up with the solutions of x = 1.618 (as aforementioned) and x = -0.618. Now, since you can't have negative length (at least that's what they say--I think I've come across it a few times woodworking), the 1.618 is the answer.

Technically, though, the solution is x = (1 ± sqrt(5))/2.

[Rob Sandow]

Well, not so much calculate as approximate. The Fibonacci sequence simply adds the last 2 numbers in the sequence to get the next, so it goes 0 1 1 2 3 5 8 13 21 34 55 89 etc. Now look at the ratio of each number to the previous number. 5:3, for example is 1.667. 13:8 is 1.625. 89:55 is 1.618. If you carry the sequence out forever and plot the ratios of each number to the previous number on a graph, you will get a curve that is asymptotic, which means it approaches but never touches a particular value. The number just keeps getting infinitesimally closer to it. That number is also referred to as a limit. The number is somewhere around 1.618, but I don't have the exact value.

[PeterTorresani]

OK the math is easy, ut explain why this ratio makes it easy on the eye. The sage advice of NAWT (Never Argue With Taste) seems to imply that there is no "golden" ratio.


Golden Rule: Who ever has the gold makes the rules.

[Philip Duffy]

So, can I measure that number with my fold up ruler???? (just kidding) Philip

[David Rose]

5/8 is a close ratio as others have shown and easier for my simple mind to remember. It's also easy to "put the ruler to". (pardon the grammar)

Dave, don't you set your FMT to cut golden ratio mortises and tenons?

David

[Dave Arbuckle]

*snork* Working on fractal M&Ts, David. Think of the glue surface!

Dave

[David Rose]

Why? My M&Ts were always a little looser than I prefered before getting the tool. By the time I trimmed off "just a teeny bit"... well, you know the drill. So tonight with the FMT they were just a touch snug. I could push them about 3/4 of the way together (5/16x1x1&1/4) then they required a heavy push to close. I went ahead and assembled two frames like this... with panels... duh! Actually there are three M&Ts per side counting a center muntin, mullion or whatever they are. And the bottom one is about double length. Guess how tough they were to get apart. Next job I plan to raise the guide pin about 2 thou, drive the pieces together and forget the glue.

David

[Ian Barley]

=PeterTorresani]OK the math is easy, ut explain why this ratio makes it easy on the eye. The sage advice of NAWT (Never Argue With Taste) seems to imply that there is no "golden" ratio.

One of the reasons that it is pleasing to the eye is that this ratio (there or there abouts) appears so often in nature. It is, on average, the relationship of the length of a quadraped to its height. It is, on average, the ratio of the width of a human face to its length. On average the human navel is 5/8ths of the way up the body. There are loads of other examples.

This means that our brains are used to seeing this kind of proportion in things and therefore process such shapes as being natural and therefore more pleasing.