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Another geometric proof proceeds as follows: We start with the figure shown in the first diagram below, a large square with a smaller square removed from it. The side of the entire square is a, and the side of the small removed square is b. The area of the shaded region is . A cut is made, splitting the region into two rectangular pieces, as ...
Throughout history, in various wars and conflicts, there have been a number of historic victories won by a smaller force, against a larger foe. Conditions and situations for these sorts of military victories against the odds have been numerous. Some victories have been pivotal to the conflict they were part of, or provided inspiration for the ...
In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial ...
Perfect square dissection, a dissection of a geometric square into smaller squares, all of different sizes Perfect square trinomials , a method of factoring polynomials Topics referred to by the same term
Dixon's method is based on finding a congruence of squares modulo the integer N which is intended to factor. Fermat's factorization method finds such a congruence by selecting random or pseudo-random x values and hoping that the integer x 2 mod N is a perfect square (in the integers):
World War II [b] or the Second World War (1 September 1939 – 2 September 1945) was a global conflict between two coalitions: the Allies and the Axis powers. Nearly all the world's countries—including all the great powers—participated, with many investing all available economic, industrial, and scientific capabilities in pursuit of total war, blurring the distinction between military and ...
For instance, the polynomial x 2 + 3x + 2 is an example of this type of trinomial with n = 1. The solution a 1 = −2 and a 2 = −1 of the above system gives the trinomial factorization: x 2 + 3x + 2 = (x + a 1)(x + a 2) = (x + 2)(x + 1). The same result can be provided by Ruffini's rule, but with a more complex and time-consuming process.
A world war is an international conflict that involves most or all of the world's major powers. [1] Conventionally, the term is reserved for two major international conflicts that occurred during the first half of the 20th century, World War I (1914–1918) and World War II (1939–1945), although some historians have also characterized other global conflicts as world wars, such as the Nine ...