SEMIOTIC - MATHEMATICAL; Step-Length Optimization Model Based on One Hasta (45 cm): Quadratic Model, Triangle Area, and Predictions to Be Tested Medically

Background: The Lancet Public Health 2025 meta-analysis (Ding et al.) reported that 7000 steps/day is associated with lower risks of mortality, cardiovascular disease, and dementia compared with 2000 steps/day. Lancet did not establish a conversion from steps to distance traveled. Objective: To propose a simple mathematical model based on 1 hasta = 45 cm to predict distance and parameters related to pathological/elderly stepping. Methods: The model is built from one quadratic function and one linear function for triangle area. No clinical testing is performed in this manuscript. Model Results: From f(x) = -x^2 + 45x + 1/4, we obtain D = 2026, vertex 506.5 at x = 22.5, roots x approx -0.0055 and x approx 45.0055. From f(x) = -2x + 90, we obtain area 2025 on the interval [0,45]. The centroid of triangle (0,0), (45,0), (0,90) is (15,30). Conclusion: This manuscript proposes the model and its predictions. Whether the predictions match patient data is the task of future medical testing, not a claim proven in this manuscript. Keywords: hasta, 7000 steps, quadratic model, centroid, prediction