Standards in this domain:

• G-MG.1
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• G-MG.2
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• G-MG.3
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• IA.8.
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• IA.9.
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• IA.10.

Apply geometric concepts in modeling situations

• G-MG.1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).^★
• G-MG.2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).^★
• G-MG.3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).^★

(IA) Use diagrams consisting of vertices and edges (vertex-edge graphs) to model and solve problems related to networks.

• IA.8. Understand, analyze, evaluate, and apply vertex-edge graphs to model and solve problems related to paths, circuits, networks, and relationships among a finite number of elements, in real-world and abstract settings.^★
• IA.9. Model and solve problems using at least two of the following fundamental graph topics and models: Euler paths and circuits, Hamilton paths and circuits, the traveling salesman problem (TSP), minimum spanning trees, critical paths, vertex coloring.^★
• IA.10. Compare and contrast vertex-edge graph topics and models in terms of:^★
  • properties
  • algorithms
  • optimization
  • types of problems that can be solved