Refer to the geometric figures below: Identify the finite geometries described by the following statements/axioms/theorems. a. There are exactly 4 distinct points in the geometric figure. b. Every line in the geometric figure has exactly three points on it. c. Each point in the geometric figure lies on exactly three lines. d. It is the geometric figure with the most number of lines among the geometries. e. The number of points & lines in the geometric figure are equal. #

Many smartphones are now able to use information sent out by GPS satellites (of which there are about nine overhead at any one time) in a similar way. Since the satellites are moving around in space, and therefore can’t be located on a two-dimensional map of the Earth, we now need to consider three-dimensional geometry. How many satellites are needed to be sure of the location of a smartphone? Explain your findings