Topic 3 in Maths AI emphasises practical geometry: mensuration, navigation (bearings), Voronoi diagrams, and trigonometry in real contexts such as surveying, architecture, and network analysis.
Volume and surface area of 3D solids: prisms, cylinders, pyramids, cones, spheres, hemispheres, and combined shapes. Applications in packaging design, construction, and manufacturing. Optimisation: finding dimensions that minimise material for a given volume.
Sine rule and cosine rule applied to real-world triangulation: surveying land, finding heights of buildings, navigation bearings. Angles of elevation and depression. Three-dimensional problems: finding angles and distances in pyramids, boxes, and terrain.
Unique to Maths AI: Voronoi diagrams partition a plane into regions based on nearest-site distance. Applications: hospital catchment areas, cell tower coverage, retail store location. Finding boundaries (perpendicular bisectors), adding new sites, and using the nearest-neighbour interpolation. Toxic waste dump problem.
Graphs, vertices, edges, degree. Euler paths and circuits. Hamiltonian paths. Minimum spanning trees (Kruskal\'s and Prim\'s algorithms). Chinese postman problem. Travelling salesman problem (nearest neighbour, upper/lower bounds). Adjacency matrices.
Voronoi diagrams divide a plane into regions based on proximity to a set of points (sites). Each region contains all points closest to a particular site. They appear only in Maths AI because they emphasise real-world spatial applications (coverage planning, resource allocation) rather than abstract mathematics. In exams, you may need to identify the nearest site, add a new site, or calculate the area of a Voronoi cell.
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