The Pythagorean Approach
to Problems of Periodicity in Chemistry and
Nuclear Physics
D.
Weise
Key words: The
periodic law, the shell nuclear model, magic numbers, figurate numbers,
Pascal's Triangle, the interdisciplinary approach.
D. I. Mendeleyev formulated
the Periodic law in 1869. The shell nuclear model was first proposed by
physicists J. Hans D. Jensen and Maria Goeppert Mayer working independently
in 1949. Both these scientific approaches are united by the concept of
Magic numbers^{*.}
Is there connection between
magic and figurate numbers? If this connection exists, in what figures
is it possible to combine magic numbers?
The present work written
specially for VM magazine, represents an attempt to select graphic images,
to deduce the analytical formulas for the mentioned scientific abstraction
and to establish some interdisciplinary connections.
*
Magic numbers in physics, in
the shell models of both atomic and nuclear structure, any of a series
of numbers that connote stable structure. They designate the sum of electrons
in atoms or the sum of either protons or neutrons in nuclei that occupy
completely filled, or closed, shells.
The
magic numbers for atoms are 2,
10, 18, 36, 54, and 86, corresponding to the total number of electrons
in filled electron shells.
The magic
numbers for nuclei are 2, 8, 20, 28, 50, 82, and 126, corresponding to
the total number of protons or neutrons in filled nuclear shells.
(Britannica)
**Among
the many relationships of numbers that have fascinated man are those that
suggest (or were derived from) the arrangement of points representing numbers
into series of geometrical figures. Such numbers, known as figurate or
polygonal numbers, appeared in 15thcentury arithmetic books and were probably
known to the ancient Chinese; but they were of especial interest to the
ancient Greek mathematicians. To the Pythagoreans (c. 500 BC), numbers
were of paramount significance; everything could be explained by numbers,
and numbers were invested with specific characteristics and personalities.
Among other properties of numbers, the Pythagoreans recognized that numbers
had "shapes."
(Britannica)
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