Most of us have heard of the “golden ratio”, but how do you quickly apply it in woodworking? Below two experts offer an explanation, courtesy of our friends at the Woodworker’s Journal:
Q. I would appreciate it if anyone could provide the formula for calculating golden ratio proportions when designing furniture. I have an old article on golden ratio, but it doesn't describe a 'how-to,' step-by-step approach. The problem I encounter is that a piece of furniture's intended use usually dictates either a height, width or depth requirement. I know one or two of these dimensional requirements, and would appreciate a formula that supplies me with a 'golden' aspect when either height or width is known."
A. (Ellis Walentine) "The golden ratio is a constant: 1.618. What's odd about it, among other things, is that .618 is to 1 as 1 is to 1.618. Divide the height of your dresser or table by this number to arrive at the prescribed width."
A. (Michael Dresdner) "Fair enough. The ratio of height to width or width to height (either way works) is 1.618 to 1 (or simply .618:1 - same thing). Simply put, pick your width and multiply it by .618 to get the height, or vice versa. I often cheat by approximating it with any two numbers from the Fibonacci sequence. It works once you get above 8 and is close enough to the golden mean to pass.
For the non-mathematical (read: non-geeks) out there, you generate a Fibonacci sequence by adding the last two numbers in the sequence to get the next number. Starting with 1, it would be as follows: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on. (3 = 2+1, 5 = 3+2, 8=5+3, etc.) Take any two adjacent numbers - 21 and 34 for instance - and you will find they closely approximate the golden mean ratio."
From the Woodworker's Journal eZine archives
Technically speaking, the 1.618 figure given above is an approximation of the ratio, but it’s definitely close enough for woodworking. For more information, the Wikipedia article covers the topic in about as much depth as any of us would want and is very readable. There’s an excellent discussion of the topic as it relates to furniture design in Graham Blackburn’s Jan., 2004 article, “A Guide to Good Design: Pleasing Proportions Borrowed From Nature.” You can access the article on Fine Woodworking website, provided you’re willing to pay a modest subscription fee (which does give you access to some very useful information). For an excellent all-around resource on how math figures in woodworking, you won’t do better than the Practical Math Dictionary. Author Norman J. Chenier covers a lot of territory, offering practical applications, tips, tricks, and just the right amount of explanation.