👉 Bus math blends linear algebra, geometry, and combinatorics to solve real-world routing problems. It models buses as points or vectors on a plane, using coordinates to represent stops and distances between them. By applying vector addition (to find new arrival points), dot products (to calculate headways or overlaps), and linear transformations (for dynamic rerouting), it optimizes schedules. For example, the "trip assignment problem" uses matrices to match passengers to buses efficiently, while "shortest path algorithms" (like Dijkstra's) determine optimal routes. This math ensures buses minimize wait times, maximize coverage, and adapt to real-time changes like traffic or passenger demand.