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The grid method (also known as the box method) of multiplication is an introductory approach to multi-digit multiplication calculations that involve numbers larger than ten. Because it is often taught in mathematics education at the level of primary school or elementary school , this algorithm is sometimes called the grammar school method.
In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144."
An example of multiplying 34 by 13 would be to lay the numbers out in a grid as follows: × 30 4 10 300: 40: 3 90: 12: and then add the entries. Computer algorithms
A grid is drawn up, and each cell is split diagonally. The two multiplicands of the product to be calculated are written along the top and right side of the lattice, respectively, with one digit per column across the top for the first multiplicand (the number written left to right), and one digit per row down the right side for the second multiplicand (the number written top-down).
0, 4, 8, 16, 32, 48, 72, 88, 120, 152, 192 … (sequence A175341 in the OEIS ). Using the same ideas as the usual Gauss circle problem and the fact that the probability that two integers are coprime is 6 / π 2 {\displaystyle 6/\pi ^{2}} , it is relatively straightforward to show that
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