The perfect squares appear in a diagonal in the multiplication table.
The second application is to foster an understanding of the wide range of patterns in the multiplication table, including the commutative property of multiplication, perfect squares, and the relationship between multiplication and division.
Thus, the triangles whose areas are perfect squares
must be such that
In other words, how far from a perfect square
can a timber deviate before the model and coefficients should be changed from the square to the rectangular mode?
These were shaped and polished into perfect squares
and the possessor of a matched set of marble gobs wouldn't have swapped one for all of Liz Taylor's diamonds.
The current standard for detecting changes in the retina from AMD is the Amsler grid, which is simply a pattern of intersecting straight lines that form perfect squares
Small spaces between pieces of Styrofoam often made interesting elements in the final prints, so there was no need to cut the plates into perfect squares
or tape them together for symmetrical grids.
For example, in Francesco Pona's treatise of 1622, II Paradiso de' Fiori, he strongly recommends that if there is a choice, then the garden should be arranged in "four perfect squares
,"(73) the standard format of the fifteenth-and sixteenth-century gardens.
Mathematicians reached a milestone in algebraic number theory by proving the local Langlands correspondence, a conjecture that concerns prime numbers and perfect squares
One of the most important results of elementary number theory is the so-called law of quadratic reciprocity, which links prime numbers (those evenly divisible only by themselves and one) and perfect squares
(whole numbers multiplied by themselves).
As an instance of the misleading behavior of small numbers, Guy cites the fact that 10 percent of the first 100 numbers are perfect squares
(1, 4, 9, 16, 25, 36, 49, 64, 81 and 100).