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A graph of isotope stability, with some of the magic numbers. In nuclear physics, a magic number is a number of nucleons (either protons or neutrons, separately) such that they are arranged into complete shells within the atomic nucleus. As a result, atomic nuclei with a "magic" number of protons or neutrons are much more stable than other nuclei.
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.
A graph is vertex-magic if its vertices can be labelled so that the sum on any edge is the same. It is total magic if its edges and vertices can be labelled so that the vertex label plus the sum of labels on edges incident with that vertex is a constant. There are a great many variations on the concept of magic labelling of a graph.
In their book, Kathleen Ollerenshaw and David S. Brée give a method of construction and enumeration of all most-perfect magic squares. They also show that there is a one-to-one correspondence between reversible squares and most-perfect magic squares. For n = 36, there are about 2.7 × 10 44 essentially different most-perfect magic squares.
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 ...
In Figure 6, for example, which is magic on rows and columns only, the 16 pieces form a so-called self-tiling tile set. Such a set is defined as any set of n distinct shapes, each of which can be tiled by smaller replicas of the complete set of n shapes. [14] A second example is Figure 4, which is a so-called 'self-interlocking' geomagic square.
The numbers of nucleons for which shells are filled are called magic numbers. Magic numbers of 2, 8, 20, 28, 50, 82 and 126 have been observed for neutrons, and the next number is predicted to be 184. [6] [27] Protons share the first six of these magic numbers, [28] and 126 has been predicted as a magic proton number since the 1940s. [29]
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For example, the magic square shown below has a magic constant of 15.