Albert Girard was the first to make the observation, describing all positive integral numbers ( not necessarily primes ) expressible as the sum of two squares of positive integers; this was published posthumously in 1634.
22.
"It is well known that the scattering from a potential shows characteristics peaks, as a function of energy, for such values of E that make the integral number of wave lengths sit within the potential.
23.
Fourier series analysis doesn't work very well if you only have a short time length of data and the data doesn't cover an exact integral number of periods, or if you are not exactly sure what the period is.
24.
For this reason, Shannon Fano is almost never used; Huffman coding is almost as computationally simple and produces prefix codes that always achieve the lowest expected code word length, under the constraints that each symbol is represented by a code formed of an integral number of bits.
25.
The Hasty Pudding cipher can also be used to encrypt values in a range that do not translate to strings with an integral number of bits; for instance, it can encrypt a number from 0 to N by producing another number from 0 to " N ".
26.
However, awk will probably not call write ( 2 ) for each line separately, but will buffer them until they reach some size ( 4 KiB is common ) and then write that much at once ( which will not be an integral number of lines, so you lose ).
27.
Euclid does not define the term " measure " as used here, However, one may infer that if a quantity is taken as a unit of measurement, and a second quantity is given as an integral number of these units, then the first quantity " measures " the second.
28.
Two key developments in the modeling of the modern ?-helix were ( 1 ) the correct bond geometry, thanks to the crystal structure determinations of amino acids and peptides and Pauling's prediction of " planar " peptide bonds; and ( 2 ) his relinquishing of the assumption of an integral number of residues per turn of the helix.
29.
A popular myth is that rolled knurls are somewhat more complicated to design than cut knurls because the outer diameter of the work piece must be chosen to allow the roller to roll an integral number of patterns around the workpiece, in practice if the knurl is applied positively, it will engage with its own impression and create a proper knurl on any diameter of work.
30.
When the two waves are in phase, i . e . the path difference is equal to an integral number of wavelengths, the summed amplitude, and therefore the summed intensity is maximum, and when they are in anti-phase, i . e . the path difference is equal to half a wavelength, one and a half wavelengths, etc ., then the two waves cancel and the summed intensity is zero.
