Allometric Scaling Inspection Through Figurate Numbers

Abstract Allometric scaling is a widely-studied, and discussed phenomena in biology that relates the parameters with a power function. There is still space for further investigation. Accordingly, the relationship is aimed to be explained for the first time in this work, through the figurate numbers, specifically the triangular, square, pentagonal, and hexagonal numbers. These mathematical series have not been considered in terms of a possible relation with allometric scaling, which is a mathematical relation in essence. We formulated the possible means of the relation of these figurate numbers with allometric scaling and suggested that their utilization can end up in different exponents and constant multipliers at varying scaling ranges. We also discussed further implications and exemplified the possible association with the blood flow-related metabolic rate adaptation. It is revealed that figurate numbers are having an inherent relation with the allometric scaling.