A geometric figure is connected if it is all in one piece. The mathematically exact definition of connected is:
Definition: A geometric figure is connected if and only if, for any two points in the figure, a path exists between the points that does not leave the figure. If a figure is not connected, it is disconnected.

Consider a figure 8. One can select any point and follow a path to any other point, even on the other side of the 8. A figure 8 is a connected geometric figure. Now consider the letter 'i' as a geometric figure. Select a point on the dot above the i. There is no path to the main part of the i that does not leave the dot. The letter 'i' is a disconnected figure. 

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