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Section 1.3 Four-Point Geometry

Figure 1.3.1. A model for the four-point geometry.

A geometric model for incidence geometry that feels more geometric is shown in Figure 1.3.1. This model is known as the four-point affine plane. An alternate version is shown in Figure 1.3.2. Are these models the same? What about the model shown in Figure 1.3.3?

Figure 1.3.2. Another model for the four-point geometry.
Figure 1.3.3. Yet another model for the four-point geometry.