A Geometric Interpretation of the Pareto Principle: Surface Growth and Cumulative Advantage

Gennady Aleksandrovich Grachev

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A Geometric Interpretation of the Pareto Principle: Surface Growth and Cumulative Advantage

G. A. Grachev

2026-04-16

https://doi.org/10.24108/preprints-3114975

This paper proposes a geometrically motivated phenomenological interpretation of the mechanism underlying Pareto-like concentration of outcomes. As a macromodel, it considers the growth of a snowball, in which the increase in volume occurs through the attachment of new particles to the outer surface of the body. It is shown that the natural coordinate of this process is the equivalent radius defining the accretion of the outer layer, while volume and mass are functions of that coordinate. The result already accumulated becomes a factor in subsequent growth because it determines the area of the active capture surface and, more generally, the system's capacity for further accumulation. For a self-similar body of dimension D, this leads to a dimensional concentration formula which, in a normalised linear coordinate, coincides with the Burr III curve for a = D and, when D = 3, naturally yields a proportion close to the 20/80 rule. The snowball effect thus acquires not only a vivid metaphorical meaning but also a geometrically grounded interpretation as a mechanism of cumulative accumulation. At the same time, the analytical form of concentration is determined by the self-similar geometry of growth, while surface accretion gives it a natural physical meaning.

Ссылка для цитирования:

Grachev G. A. 2026. A Geometric Interpretation of the Pareto Principle: Surface Growth and Cumulative Advantage. PREPRINTS.RU. https://doi.org/10.24108/preprints-3114975

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