Examination of a Sigmoid Shape Composition for BMI Fluctuation and Fat Percentage

Body mass index (BMI) is an index of physique proposed by Quetelet, and has been given meaning as the Quetelet function, which is the ratio of body weight to the square of height. In recent years, BMI has been considered an indicator of obesity due to its high correlation with body fat percentage. However, while the relationship between BMI and body fat percentage shows a high correlation, the composition of that relationship is not well understood. Moreover, there is almost no information on the relational composition in males and females. In this study, we investigated that relational composition to determine whether the relationship between BMI and body fat percentage follows a linear trend or a curvilinear trend. For that purpose, we analyzed the changes in body fat percentage associated with fluctuations in BMI. For BMI fluctuations, the body fat percentage of the scale width of one BMI unit was calculated when BMI was increased one unit at a time, and the changes in the calculated statistics were analyzed. The type of function series to which the relationship between BMI and body fat percentage fits was then verified. The results demonstrated that in males the fluctuations in body fat percentage with respect to BMI show a sigmoid shape. In males, when BMI exceeds 25, the velocity of body fat percentage decreases and soon reaches a constant level. A sigmoid curve is thought to be a finding that means a critical point in the inflection point phenomenon. Therefore, the fact that the change in body fat percentage with respect to BMI shows a sigmoid shape means that, in males, body fat percentage shows a critical point at a BMI of 25. In females, however, the critical point is a BMI of 28.6 and body fat percentage reaches a constant level when a point higher than that in males is exceeded, but the shape could not be judged to be sigmoid. There are limits to BMI for humans, we propose a limiting body fat percentage hypothesis in which body fat percentage becomes constant from a BMI of around 32.