Section 9.3: Topology and Fractals

9.3 Outline

  1. Topology
    1. topologically equivalent figures
    2. planar curve
    3. closed curve
    4. interior/exterior
    5. simple curve
    6. Jordan curve
    7. invariant property
    8. genus
  2. Four-color problem
  3. Fractal geometry
  4. Tessellations

 

9.3 Essential Ideas

Two geometric figures are said to be topologically equivalent if one figure can … See the whole entry

Section 9.1: Euler Circuits and Hamiltonian Cycles

9.1 Outline

  1. Euler circuits
    1. Konigsberg bridge problem
    2. definition of a graph (or a network)
    3. traversable network
    4. degree of a vertex
    5. Euler circuit
    6. odd/even vertex
    7. connected network
    8. Euler’s circuit theorem
  2. Applications of Euler circuits
    1. supermarket problem
    2. police patrol problem
    3. floor-plan problem
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