WiFi Signal Strength Using Geometry: Using Smartphones to Map WiFi Signal Strength and Applying Mathematical Models to Predict Dead Zones and Optimize Router Placement

Optimizing WiFi router placement has become crucial for ensuring seamless network coverage with the increasing reliance on wireless internet connectivity in homes and schools. This research investigates the geometric patterns of WiFi signal strength distribution and develops mathematical models to predict dead zones and optimize router placement using smartphones as measurement devices. Through systematic data collection across various indoor environments, we analyzed signal strength patterns using inverse square law modifications, geometric modeling, and statistical regression analysis. Our findings demonstrate that WiFi signal propagation follows

predictable mathematical patterns that can be modeled using modified exponential decay functions with obstacle interference coefficients. The developed models achieved 85% accuracy in predicting signal strength at untested locations and successfully identified optimal router placement positions that reduced dead zones by an average of 40%. This research provides practical tools for improving WiFi coverage in residential and educational settings using readily available smartphone technology.