The Functions of Numbers chart (figure 1-27 {and 1-27b) is included in this chapter for convenience in making computations. Familiarization with the various parts of this chart will illustrate the advantages of using "ready made" computations.

Numbers

The number column contains the numbers 1 through 100. The other columns contain computations for each number.

Square

Square is the product obtained by multiplying a number by itself: 1 x 1 = 1, 2 x 2 = 4, 17 x 17 = 289. Squaring may be considered a special form of area computation: Area = Length multiplied by Width, A = L x W.

Cube

Cube is the product obtained by multiplying a number by itself, then multiplying that product by the number again: 1 x 1 x 1 = 1, 2 x 2 x 2 = 8, 13 x 13 x 13 = 2,197. Cubing may be considered a specialized form of volume computation: Volume = Length multiplied by Width by Height, V = L x W x H.

Square Root

Square root is the opposite of a "squared" number. The square root of a number is, that number which when multiplied by itself (squared) will produce the original or desired number: For example, the square root of 1 is 1, 1 x 1 = 1. The square root of 4 is 2. The square root of 24 is 4.8990. If an area of 24 square inches must be a perfect square, the length of each side would be 4.8990 inches.

Cube Root

A cube root is the opposite of a "cubed" number. The cube root of a number is that number which when multiplied by itself (cubed) will produce the original or desired number. The cube root of 1 is 1, 1 x 1 x 1 = 1. The cube root of 27 is 3, 3 x 3 x 3 = 27. If a container of 100 cubic inches and cubic in shape is desired, then the length of each side would be 4.6416.

Circumference of A Circle

Circumference is the linear measurement of the distance around a circle. The circumference is calculated by multiplying the diameter of the circle by the constant 3.1416 (). This constant was calculated by dividing the circumference of circles by their diameter. For example, diameter = 1, circumference = 3.1416, 1 x 3.1416 = 3.1416. Diameter = 10, 10 x 3.1416 = 31.4160, diameter = 12, 12 x 3.1416 = 37.699.

Area of A Circle

Area of a circle is the number of square units of measurement contained in the area circumscribed by a circle of the diameter of the listed number. This is calculated by the formula x r2 = a, pi multiplied by the radius squared equals area. The radius is equal to one half the diameter. For example, diameter = 2, radius = 1. 3.1416 x 1 = 3.1416 square units in a circle which has a diameter of 2. Another example, diameter = 4, radius = 2. 3.1416 x 22 = 3.1416 x 4 = 12.5664 square units.