Weight/height²: Mathematical overview of the world's most widely used adiposity index

A footnote in Adolphe Quetelet's classic 1835 Treatise on Man described his algebraic analysis of how body weight ( $W$ ) varies with height ( $H$ ) in adult males and females. Using data on 12 short and 12 tall subjects of each sex, Quetelet established the rule that $W$ is approximately proportional ( $\propto$ ) to H² in adults; that is, $W\propto H^2$ when $W\approx \alpha H^2$ for some constant $\alpha$ . Quetelet's Rule ( $W\propto H^2$ ), transformed and renamed in the twentieth century to body mass index ( $\mathrm{BMI}=W/H^2$ ), is now a globally applied phenotypic descriptor of adiposity at the individual and population level. The journey from footnote to ubiquitous adiposity measure traveled through hundreds of scientific reports and many more lay publications. The recent introduction of highly effective pharmacologic weight loss treatments has heightened scrutiny of BMI's origins and appropriateness as a gateway marker for diagnosing and monitoring people with obesity. This contemporary context prompted the current report that delves into the biological and mathematical paradigms that underlie the simple index $\mathrm{BMI}=W/H^2$ . Students and practitioners can improve or gain new insights into their understanding of BMI's historical origins and quantitative underpinning from the provided overview, facilitating informed use of BMI and related indices in research and clinical settings.