QUARTER SQUARES

method of computing the product of two numbers, which can be expressed as the difference of one-fourth the squares of their sum and their difference: ab = 1/4(a + b)2 - 1/4(a - b)2. This fact has been used to reduce multiplication to addition with the aid of tables of quarter squares or with other methods of generating quarter squares. The quarter square of an odd number always has a fractional part 1/4, which can be ignored in applying the formula. The method is very old, and many tables of quarter squares have been prepared; however, few tables are easily available. The most extensive table lists quarter squares of integers not exceeding 200,000. Various mechanical and electrical applications have been suggested. The method is still frequently useful and economical.