Chapter 8 Elements and Principles of Interior Design 237 Copyright Goodheart-Willcox Co., Inc. comparison of two wholes to each other. Here are some examples. ■ External and internal relationships. Scale identifies external relationships—the size of human body to an object. Proportion describes internal relationships such as the size of ears on a human head. ■ Function and perceived beauty. Scale in interiors often relates to the function of space. Proportion in interiors typically relates to perceived beauty within the composition. People often reference scale in everyday language when discussing small scale or large scale objects. The human body, however, is not a static standard, Figure 8-27. It changes size, so there are a variety of scales with which to compare. For example, if you visit your child- hood home after growing to your adult height, you will notice how much smaller the house is in comparison to you. A chair that accommodated your size then does not fit you now. Do you remember the childhood story Goldilocks and the Three Bears? Goldilocks tested out three differently sized chairs to find one that fit “just right.” That story is an example of scale. D E S I G N E R M A T H S K I L L S Golden Mean Have you ever thought about how many rectangles there are in your daily life? Some examples include a cell phone, a debit card, a dollar bill, a textbook, and even a piece of notebook paper. Calculating Ratios Squares have sides of equal distance creating a 1:1 ratio. Rectangles have two unequal sides, but are more appealing and harmonious to the eye than squares. 3 ÷ 3 = 1:1 ratio 5 ÷ 3= 1:1.66 ratio (round up to 1:1.67) For example, a 5'-0" × 7'-0" area rug (1:1.4 ratio) is more appealing than a square 7'-0" × 7'-0" area rug (1:1 ratio). How does a designer determine ratio? It is actually quite easy—just divide the larger number by the smaller number. A ratio can be written with a colon (:) or using the word to such 1:1 or 1 to 1 ratio. A 3" × 5" index card has a 1:1.66 (1:1.67 rounded up) or 1 to 1.67 ratio. Note that a 5" × 7" picture frame has the same ratio as the 5'-0" × 7'-0" rug. Calculating Proportion Using the Golden Mean Ratio defi nes proportion. For centuries a ratio called the Golden Mean (1:1.618) has been used for determining proportions. In interior design, you can use the Golden Mean to determine how high to hang pictures or wall accessories, the height of a chair rail, or where to place drapery tiebacks. To calculate the height to hang a picture, poster, or a shelf in a room with 9' (108") ceiling, you divide the ceiling height by the golden mean. 108" ÷ 1.618 = 66.74" (rounded up to 66.75" or 66 3/4"). The object is hung 66 ¾" up from the fl oor. To determine the height of a chair rail in the same room, you can measure down from the ceiling 66 ¾" (or 41 ¼" up from the fl oor). See the following example. 1" 1" 3" × 3" 3" × 5" 1" 1.67" Ceiling Floor 108" Shelf height = 66.75" from floor Chair-rail height = 41.25" from floor