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For instance, the magic number 8 occurs when the 1s 1/2, 1p 3/2, 1p 1/2 energy levels are filled, as there is a large energy gap between the 1p 1/2 and the next highest 1d 5/2 energy levels. The atomic analog to nuclear magic numbers are those numbers of electrons leading to discontinuities in the ionization energy.
A magic circle can be derived from one or more magic squares by putting a number at each intersection of a circle and a spoke. Additional spokes can be added by replicating the columns of the magic square. In the example in the figure, the following 4 × 4 most-perfect magic square was copied into the upper part of the magic circle. Each number ...
Such signatures are also known as magic numbers or magic bytes. Many file formats are not intended to be read as text. If such a file is accidentally viewed as a text file, its contents will be unintelligible. However, some file signatures can be recognizable when interpreted as text.
The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3. In mathematics, especially historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same.
For example the following sequence can be used to form an order 3 magic square according to the Siamese method (9 boxes): 5, 10, 15, 20, 25, 30, 35, 40, 45 (the magic sum gives 75, for all rows, columns and diagonals). The magic sum in these cases will be the sum of the arithmetic progression used divided by the order of the magic square.
The number zero for n = 6 is an example of a more general phenomenon: associative magic squares do not exist for values of n that are singly even (equal to 2 modulo 4). [3] Every associative magic square of even order forms a singular matrix, but associative magic squares of odd order can be singular or nonsingular. [4]