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 be elastically twisted, stretched, bent, shrunk, or straightened into the same shape as the other. One can cut the figure, provided at some point the cut edges are “glued” back together again to be exactly the same as before.

Other ideas discussed in this section are the four-color map coloring problem, fractals, and tessellations.