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Golden section is the division of a length at which the ratio of the division to the whole is equal to the ratio of the smaller division to the longer.
18th century craftsmen very likely determined golden section by using a simple divider trick. Given an established dimension (the width of a piece of stock for example), the dividers are set to a whole number fraction and that number is recorded. That distance is then marked along the edge of a board. The dividers are reset to Ã?½ the previous setting and a triangle is constructed 1 wide by Ã?½ high. The hypotenuse is struck and Ã?½ is marked along its length (from either end doesn’t matter). The portion of the hypotenuse remaining is golden section of the original.
Once you find golden section, you walk your dividers the same number of movements you used to establish your divider setting initially and you’ve got an accurate answer. For carcass sized dimensions, I often use a tape measure and my calculator. But for smaller things, maybe only a few inches across, it can be more accurate to use dividers and its really not much slower.
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Thanks for this technique, Adam. Being a bit of a midget in both theoretical and practical mathmatics, I’m always glad to learn tricks like this, which may be obvious to others but are in no way obvious to me.
Hi Adam
Glad to see you’ve got your own Blog! I enjoy your A+M articles (as well as your input on the woodworking forums!)
The golden section is a handy design rule-especially if you break it!! By making a piece only a small amount larger or small you can really alter the "feel" of a piece (i.e. "tall", "fat")
best regards
Phil