Popular Woodworking 2003-12 № 138, страница 72
Even casework, such as this clock, with its complex mouldings and carvings, will fit within a golden rectangle, as shown by the blue line. Proportion is the size relationship between various parts, as well as from those parts to the entire piece. For example, the feet on a desk or chest should appear in proportion to the casework. If the feet are too small, the casework will visually overpower them and make them appear weak or fragile. If the feet are too large, they can make the chest appear awkward or clumsy. Mouldings, doors, drawers and other details must all be in correct proportion if the work is to be a visual success. But how do you create good proportions when designing furniture? One way is to use mathematical systems. You've probably heard of the golden section (also called the golden ratio): It's a ratio (1:1.618) that's found in many natural objects - including the human body - that's been used for centuries by artists, designers, architects and craftsmen. The Golden Section The golden section was discovered by the ancient Greeks and is still widely used today. Not surprisingly, the ratio of the golden section, 1:1.618, is very close to the ratio of 5:8, two of the numbers in the Fibonacci series (which we'll discuss later). Of course, the ratio of the golden section can be used to create a golden rectangle. You can find the golden rectangle in a wide variety of well-proportioned items, both natural and man-made. For example, the facade of the Greek Parthenon fits within the golden rectangle. A credit card (218" x 33/s") also fits within a golden rectangle. And many items found in nature fit within a golden rectangle. Here's an interesting twist to try on your own - draw a square within a golden rectangle and the rectangle that remains also will be a golden rectangle. Begin with a Rectangle When designing a new piece of furniture, I typically start with a rectangle. That's because all furniture, tables, casework and even chairs will fit within a rectangle. Often, the first dimension of a rectangle is given. For example, the writing surface of a desk is typically 30" high. If you make it higher or lower, it becomes impractical for use. Dining tables also are 29" to 30" high; chair seats are usually 17" from the floor. (For more standard sizes look below and on the following page.) To find the second dimension of the rectangle, I use a numbering system. For example, for a 30"-high table, multiply 30" x 1.618, which yields a table length of approximately 481/2". After drawing the rectangle I scale the elements within the rectangle, such as feet, doors, drawers, carvings and mouldings. To help me find pleasing proportions, I'll often use Fibonacci numbers. Fibonacci Numbers Fibonacci was an Italian mathematician who discovered the series of numbers that bear his name. Each number in the series is added to the previous number to find the next one in the series - 1, 1, 2, 3, 5, 8, 13, etc. Interestingly, the Fibonacci series can be found everywhere - from natural objects such as nautilus seashells to common, everyday items such as with 3" x 5" index cards. Let's say you want to use ratios of Fibonacci numbers to figure out the size of a cabinet's feet. First, let's say the overall height of the cabinet is 84". Divide the height by a Fibonacci number. Which one? Take an educated guess. Determining which number to use comes with experience. My first guess would be to divide the number by 13, which means my cabinet's feet would be about 61/2" high. (Don't hesitate to add or subtract half an inch. While the numbers don't often deviate, they're also not set in stone.) If this number looks good, great. Use another number to come up with the horizontal dimension (for example, multiply the foot's height by 1.618 to get about 101/2" - see the photo on page 75). If you feel this number is too large, simply divide the cabinet's height by a larger Fibonacci number to come up with a smaller height. It's a lot of work but it's worth it. Seventy-five to 80 percent of my furniture is designed using mathematics. Fibonacci numbers also could be used to size the top of a table. For example, using the ratio of 2:3, the width of the top of a tea table could measure 18.5" and the length is 273/4" (18.5 divided by 2 times 3 equals 27.75). Arithmetic Progression If you've ever looked at a chest of drawers in which each drawer is the same size, you know how visually dull it can be. Drawers add much more visual interest to casework if they graduate, or become increasingly larger toward the bottom of the case. However, the progression used must be in proportion to the size of the casework. If the drawers popwood.com 73 |
