Sentence examples for diagonal of a square from inspiring English sources
Below is its reciprocal, the answer to the problem, that of calculating the diagonal of a square whose sides are 0.5 units.
Its members only reluctantly accepted the discovery that √2, the ratio of the diagonal of a square to its side, could not be expressed as the ratio of whole numbers.
Other discoveries often attributed to him (the incommensurability of the side and diagonal of a square, for example, and the Pythagorean theorem for right triangles) were probably developed only later by the Pythagorean school.
For example, there is no number among integers and fractions that equals the square root of 2. A counterpart problem in measurement would be to find the length of the diagonal of a square whose side is one unit long; there is no subdivision of the unit length that will divide evenly into the length of the diagonal.
In the surveying of new cities in the Greek colonies of the 6th and 5th centuries, there was regular use of a standard length of 70 plethra (one plethron equals 100 feet) as the diagonal of a square of side 50 plethra; in fact, the actual diagonal of the square is 50√2 plethra, so this was equivalent to using 7/5 (or 1.4) as an estimate for √2, which is now known to equal 1.414….
Consider the side and the diagonal of a square.
However, the reported application of PQ could have been carried out as far away as 2256 m (the length of the diagonal of a square-mile section) from the field of interest, which in itself might have been 500 m from the subject's home.
This belief was shaken, however, by the discovery that the diagonal of a unit square (that is, a square whose sides have a length of 1) cannot be expressed as a rational number.
tr(M): the sum of diagonal elements of a square matrix M. 〈·,·〉: the inner product on a Euclidean space given by 〈M,N〉↦tr(M ⊤ N). (|M|triangleq sqrt {text {tr}(MM^{top })}): the Frobenius norm of a matrix M. ({mathcal {R}}(M)): the range of a matrix M. (mathbb {R}^{ntimes m}): the Euclidean space of all n×m real matrices.
As the stiffness, strength and ductility of square box columns are almost similar around any axis, this connection is composed of vertical plates that pass through the diagonal axes of a square box-column and are welded to the box corners.
where ϕ l is the lth element of the parameter vector ϕ, (hat {phi }_{l}) is an estimate of ϕ l, for l∈{1,2,3,4}, l,l is the lth diagonal element of a square matrix, and (mathrm {I}^{-1}left [f_{mathbf {Y}_{mathbf {a}}}(mathbf {y}_{a};boldsymbol {phi })right ]) is the inverse of FIM.
