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Okay, I read the short tip in this months FL on the “golden triangle” but it doesn’t tell me what it is used for, it sounds like some sort of proportion ratio for drawers etc. I have my own methods for size and proportion but this sounded simpler. Can anyone tell me where to read more about this?
Thanks
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John,
What is "FL"? The only "golden triangle" that I've ever read about was Marilyn Monroes's. All kidding aside, I do not know the article or magizine in which you refer.
A right triangle is often used in proportional division of a line to another line of different length or can be used to divide a line into equal parts, as in layout for dove tails. In kitchen design, triangles are used in the lay out for distance travelled in the work area, the objective being to try and design around an equilateral triangle.
Can't say if it is simpler than your method.
Dano
*I thought the golden triangle was the area heroin was produced in in the far east.
*John,Do you mean the golden rectangle in "Methods of Work" FWW #148? The golden rectangle is attributed to Plato, it is considered to be a universally pleasing proportion.The Parthennon's facade fits into a golden rectangle.Leonardo da Vinci's "The Proportion of the Human Figure" falls very close to a golden rectangle, feet together, arms straight out with the navel as the dividing line.My favorite is the spiral of sea shells. If you draw a golden rectangle starting with a square (A-B-C-D) and add (E-F)like the one in FWW, then divide the smaller side (C-D-E-F) into another rectangle. Repeat this six times always rotating counter clock wise. Then draw a curved line from A to D and then to D of the next rectangle and it will form a beautiful spiral.Now if anyone from Taunton is reading, can I get a free Lie-Nielsen handplane if I regurgitate a method from one of your own magazines? i.e. Home Furniture #7and 8 1996.Chris
*MadDad,You know you could be right, thought I remembered reading about the "golden rectangle", but not in FWW. If my memory serves me correctly, the golden rectangle is in fact a trapazoid. The reason why the Parthanon is considered so well proportioned is that all verticle lines actually angle very slightly outward to reduce the effect of perspective, tricking the eye into seeing perfectly parallel lines. I could be wrong, since I am recalling course work I did in high school and college many moons ago. Also, I think the "golden rectangle" is more of a concept than an actual mathmatical formula.Dano
*The golden rectangle also caled the "Section" or golden section is a maththmatical formula. It is a proportion based on 1x1.618 Take a square of any size, if one side is A then A x 1.618 will equal the long side of your rectangle.The reason this is diferant than just a pleasing form is the way the short side of the rectangle relates to the long side in the same way that the short section B(B=.618 of A)relates to the long side.A/A+B=B/AThank God I have my old text books they make me look real smart (:ChrisDano did you get the April FWW yet
*MadDad,Thanks for the clarification, wonder what I'm thinking of?....No, I haven't, stopped subscribing years ago. Just buy the ones that have something of interest to me.Dano
*FL... where did I come up with FL? Ye, Chris I meant the "Methods of Work" FEW #148 article. As I read the responses I'm assuming the golden triangle is limited to mathematical expressions of proportions that are eye pleasing. Although I must say I am far more impressed with Dan's response relative to Marilyn!ThanksJohn Brash
*Ops, now I see the problem. I'm having some difficulty with this spell checker. Its changing the words without a confirmation back from me. Sorry for the misspellingsJohn Brasch
*DanoI think that you were thinking about Greek columns that appear to be strait but really bow out just a little to fool the eye.Chris
*No, you misremember about Marilyn Monroe: its the Golden Globe awards that were named after her.
*Curving the columns outwards allows for entasis, the tendency of the eye to see two close parallel lines as curving towards one another. The curve makes the lines appear parallel. I've noticed in the US that many columns have exaggerated curves, especially in house building, which I find unattractive. I've often wondered if the exaggeration is intentional, or just an old screw up that somehow became accepted practice. Sliante.
*SlianteI think its a continual screw up and a lot of crappy design, sutiltie is a lost art. Chris
*Chris,You are correct about the columns. I do, however, recall that the Greeks also angled the vertical elements slightly outwards as well. This now comes quite vividly to mind from an early course in architecture. It also is reinforced by images that I am seeing out of a book entitled "World Architecture". This was published by Random House, as I recall, in the mid 70's. This book is quite large and coincedently, the jacket is a photo of the Acropolis with, of course, the Parthenon on top of it. The copy I had disappeared (along with many other possessions)after my divorce 16 years ago. Any who, the reason why these images are so vivid in my mind is because of an exercise we did class about proportion using reproduced schematics and photos of the Parthenon's front and side elevations. You could actually see that the exterior walls are angled away from center. I don't recall the precise measurements but do recall that they had figured a formula. I also don't remember it being called the "golden triangle". But your description and formula does ring a bell. Just haven't figured out which bell.:) Normally, I wouldn't post something like this here without a more precise referenced text, but I'm so sure of this I decided to take the chance and leave the burden of proving me incorrect to others.Dano
*John,The "Golden Mean" was made widely known by work of a famous Italian mathmatician by the name of Leonardo de Pisa. Obviously building on the work of prior Greek builders and mathmeticians he also created his "Fabonacci" numbers which are the actual formulas by which nature (God) creates thing such as spiral seashells. Do a search on "fabonacci" and you will come upon some pretty interesting sites.Buildings were designed by mathmaticians back then and I sometimes wonder if that is why they withstood the test of time so well.That thing about Marilyn was probably an interesting site also....DDay
*John,Correct spelling..."Fibonacci"The grander the arena the greater the mistake...Derrell
*Dano, not only did the Greeks curve the columns slightly and lean the columns inwards, they even crowned the floors and lintels of their temples so it wouldn't look like they were sagging! They weren't spaced perfectly either, they're slightly closer together at the corners. Not to some scientific principle, apparently done more or less by eye on site. Had to break out my college art history book for that one....MM
*In architectural and furniture design (I teach both)we often refer to the "Golden Ratio". Basically, a specific number that is equal to it's inverse plus one. You can find it this way: Take the square root of 5. Add one. Divide by two.You'll get 1.61803398874989484820458683436564.The inverse of this number is .61803398874989484820458683436564. Add one and you have the same number.The successive numbers in the Fibonacci (2,3,5,8,13,21,34,etc) series begins to approximate this ratio as they grow larger. 8/5 is 1.6. 34/21 is 1.61904.Use this number as a multiplication factor when determining related dimensions. Building a dresser? Take your height (48", for example) and multiply it by .618... to find the width. You've just created a Golden Rectangle. A 48" x 29.7" dresser has porportions that will be appealing to a majority of people that view it.I suppose the same ratio could be used to determine sides of a triangle. One side (20") x 1.618 = second side (32.36") x 1.618 = third side (52.33"). I'm not quite sure what you'd use such a triangle for, though.If you like to justify porportions by basing them on some mathematic or natural ratio, consider the square root of two (1.414). It is close to the golden ration, but different. In furniture design I find it actually more appealing. A table top, for example, with one side 1.414 times greater than the other, will have identical porpotions when folded in half. I have a table design using this principle. The top folds up and rotates 90 degrees about a specific point to center itself perfectly on the same base in either position.Math is wonderful. Now if wood would just stick to one dimension! ;-)Dave
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