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Starting from a unit square dividing its dimensions into three equal parts to form nine self-similar squares with the first square, two middle squares (the one that is above and the one below the central square) are removed in each of the seven squares not eliminated the process is repeated, so it continues indefinitely.
For odd square, since there are (n - 1)/2 same sided rows or columns, there are (n - 1)(n - 3)/8 pairs of such rows or columns that can be interchanged. Thus, there are 2 (n - 1)(n - 3)/8 × 2 (n - 1)(n - 3)/8 = 2 (n - 1)(n - 3)/4 equivalent magic squares obtained by combining such interchanges. Interchanging all the same sided rows flips each ...
The square has Dih 4 symmetry, order 8. There are 2 dihedral subgroups: Dih 2, Dih 1, and 3 cyclic subgroups: Z 4, Z 2, and Z 1. A square is a special case of many lower symmetry quadrilaterals: A rectangle with two adjacent equal sides; A quadrilateral with four equal sides and four right angles; A parallelogram with one right angle and two ...
When the term 'grid square' is used, it can refer to a square with a side length of 10 km (6 mi), 1 km, 100 m (328 ft), 10 m or 1 m, depending on the precision of the coordinates provided. (In some cases, squares adjacent to a Grid Zone Junction (GZJ) are clipped, so polygon is a better descriptor of these areas.)
Every n-by-n Latin square has a partial transversal of size 2n/3. [11] Every n-by-n Latin square has a partial transversal of size n − sqrt(n). [12] Every n-by-n Latin square has a partial transversal of size n − 11 log 2 2 (n). [13] Every n-by-n Latin square has a partial transversal of size n − O(log n/loglog n). [14]
For n ≥ 2, the n-dimensional Wiener process started at the origin is transient from its starting point: with probability one, i.e., X t > 0 for all t > 0. It is, however, neighbourhood-recurrent for n = 2, meaning that with probability 1, for any r > 0, there are arbitrarily large t with X t < r; on the other hand, it is truly transient for n > 2, meaning that X t ≥ r for all t ...
Super Bowl Squares are the second most popular office sports betting tradition in the United States (No. 1: March Madness brackets), maybe because the outcome is based entirely on luck.
Square packing in a square is the problem of determining the maximum number of unit squares (squares of side length one) that can be packed inside a larger square of side length . If a {\displaystyle a} is an integer , the answer is a 2 , {\displaystyle a^{2},} but the precise – or even asymptotic – amount of unfilled space for an arbitrary ...