Ben Zielinski, age 15, of St. Augustine, Fla., for his question:
EXACTLY WHAT IS A SQUARE?
A square, in geometry, is a plane figure that has four equal straight sides and four right angles, or 90 degree angles. If each side of a square is four inches long, the square can be cut into four by four, or 16, smaller squares that have sides one inch long.
The area of a square that measures four by four inches, as you can see, equals 16 square inches.
In general, the area of a square is expressed in square units. It is found by multiplying by itself the number that represents the length of one side of the square. A square with a side of 12 inches long has an area of 12 multiplied by 12, or 144 square inches.
In arithmetic and algebra, the square of a quantity is the product of a quantity by itself. For example, 16 is the square of 4 because 4 times 4 equals 16.
The term square also refers to a tool or instrument for measuring and constructing right angles. Carpenters often use a square made in the shape of an "L" and draftsmen use a square in the shape of a "T."
A square deal originally referred to fair treatment in dealing playing cards and in handling other transactions. President Theodore Roosevelt used the slogan repeatedly: "When I say "square deal,' I mean a square deal to everyone." Roosevelt said that he would use his powers to safeguard the rights of both capital and labor.
A square measure is the system used in the measurement of surface. The unit for the area of a surface is the square.
We can describe a table top as being 12 inches long and 10 inches wide. But these figures represent only lines, which have just one dimension that of length.
A plane surface has two dimensions: length and width. They must somehow be combined into a single expression in order to tell how much the table will hold. Thus we describe the area of the same table top as 120 square inches. We get this figure by multiplying length by width.
The reason we come up with 120 square inches is clearly seen if we draw a picture. A line should be drawn every inch along the 12 inch length, and at every inch along the 10 inch width. The two sets of lines will cross each other. This will give us 120 little squares, each measuring one inch in length and one inch in width.
The measure of each is called a square inch. The area in square inches, feet, centimeters, meters and so on, of other geometrical figures, is found by special rules, all based on the one stated above.
Square root of a number is a second number whose product with itself gives the original number. For example, a square root of 4 is 2, because 2 times 2 equals 4.
Any easy method for finding a square root of a number is to use a table of square roots, a table of squares or a table of logarithms. These tables list a square root and make long and tiresome calculations unnecessary.
You can usually learn to use square root tables in a short time.
Another way to find a square root consists of using a slide rule. But a slide rule can usually give a square root in only three digits.