Geometry in Home Decorating

Determining Areas

• When buying new carpet for your home, you will need to determine the exact amount. Geometry can help you determine the area of a room. Measure each room you will be carpeting, and then use geometry to determine the total area of the rooms, with the formula: area equals length times width. The answer will be expressed in square feet. For example, a hallway that is 22 feet long and 5 feet wide will have an area of 110 square feet. For wallpaper, measure the height and width of each wall to get the area. Then add up the area of each wall you are papering to find the total square footage of wallpaper you need.

Area of an Alcove

• Not every room is made up of straight lines. Geometry can also help when you are decorating curved spaces in your home. To calculate the amount of carpet needed to fit in a curved space, such as an alcove, use the formula: area of circle equals pi times radius squared. The radius is one half of the diameter of the circle. To determine the radius, you measure the alcove all the way across at its widest point and then divide this number in half. So, if the alcove measures 10 feet at its widest, its radius would be 5 feet. You then square this number by multiplying it by itself. Here, you would have 5 x 5 = 25. Pi is a constant that is roughly equal to 3.14. Plug in the numbers to find the area: 3.14 x 25 = 78.5 square feet. So, if your alcove is a complete circle, its area would be 78.5 square feet. If it is a semi-circle, you would halve this number to give you an area of 39.25 square feet. That is how much carpet you need.

Golden Mean

• Many architects, such as Corbusier, have based their work on the golden mean. The golden mean is a measurement in which the length of sides of a rectangle are expressed in a ratio of 0.618 to 1.0. The Ancient Greeks believed that buildings and rooms designed using wall lengths in this ratio were more pleasing to the eye and have a calming influence. You can use this geometric principle in interior decorating by placing objects in a room so that they form shapes with this ratio. For example, to apply the golden mean to where you place a chandelier, you first measure the height of the room and then multiply this by 0.618. For a nine-foot ceiling, this would be: 108 inches by 0.618 = 66.74 inches. So, the most pleasing place to hang the chandelier would be around 67 inches from the floor.

Symmetry

• Symmetry describes a geometry where two halves of an object or space are identical. Symmetry in interior design describes a room where similar objects are balanced on either side of the room. For example, you might have identical couches on either side of a room. The balance of symmetrical spaces is thought to be soothing and relaxing. Asymmetrical balance, where different types of decorations, such as two couches of different styles, are placed to give a balanced feel can make a room feel lively and energetic. Radial symmetry, where objects are placed around a center point, such as a fireplace, add interest to a room.