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Section 3.2 Taxicab Circles

What are circles? The set of points at constant distance from the center. But we have changed the notion of distance! Two taxicab circles are shown in Figure 3.2.1.

You can change the radius of the inner circle using the slider, and that of the outer circle by moving point \(P\text{.}\)

Figure 3.2.1. Taxicab circles are squares!

You can explore constructions in taxicab geometry using the new tools in the right-most menu in Figure 3.2.2. Do not confuse these new tools with their Euclidean analogs, even though their icons are the same!  1 

The new tools are a taxicab distance function, a taxicab circle-with-radius tool, and a taxicab circle-with-point tool, labeled respectively with the (Euclidean!) icons below:
Use each of these tools as you would their Euclidean counterparts: to measure disance, select two points; to construct a circle, select the center point and either specify the radius or select a point on the circle.
Figure 3.2.2. A GeoGebra interface for taxicab geometry. (You may need to click on the menu icon in the top right and scroll in order to gain access to the new menus.)
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