So whenever we pick two rows and two columns of a Monge array and consider the four elements at the intersection points, the sum of the upper-left and lower right elements is less than or equal to the sum of the lower-left and upper-right elements.
This array is a Monge array:
For example, take the intersection of rows 2 and 4 with columns 1 and 5. The four elements are:
17 + 7 = 24 23 + 11 = 34
It holds that the sum of the upper-left and lower right elements is less than or equal to the sum of the lower-left and upper-right elements.
Monge arrays are useful for keeping growth of functions in O(nlog n) time or less.
An officer of engineers seeing it wrote to recommend Monge to the commandant of the military school at Mézières, and he was received as a draftsman and pupil in the practical school attached to that institution; the school itself was of too aristocratic a character to allow of his admission to it.
Monge's memoir just referred to gives the ordinary differential equation of the curves of curvature, and establishes the general theory in a very satisfactory manner; but the application to the interesting particular case of the ellipsoid was first made by him in a later paper in 1795.
Gaspard Monge died at Paris on July 28, 1818 and was interred in Le Père Lachaise Cemetery in Paris, in a mausoleum.
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