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In two dimensions, 2x 1 + 2x 2 is the perimeter of a rectangle with sides of length x 1 and x 2. Similarly, 4 √ x 1 x 2 is the perimeter of a square with the same area, x 1 x 2, as that rectangle. Thus for n = 2 the AM–GM inequality states that a rectangle of a given area has the smallest perimeter if that rectangle is also a square.
Soal moved to a more statistical and controlled approach, firstly by conducting an experiment in which up to a few hundred persons participated at one time. [5] This involved Soal and a small group of agents enacting a scenario, playing with a certain object, reciting a poem, and so on, which the participants, situated across Great Britain and other countries, were required, at the same time ...
In the same way, an extension K 2 of K 1 can be constructed, etc. The union of all these extensions is the algebraic closure of K , because any polynomial with coefficients in this new field has its coefficients in some K n with sufficiently large n , and then its roots are in K n +1 , and hence in the union itself.