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The maneuver that involves flying in circular paths around two selected points on the ground is known as Eights on Pylons. This maneuver is designed to improve a pilot's precision and coordination skills by requiring them to maintain a constant altitude and airspeed while flying two circles, one around each of the selected points.

The aircraft is maintained in a balance of performance that requires continuous adjustments to control inputs as the pilot navigates between the two points. By practicing this maneuver, pilots learn how to manage bank angles and airspeed effectively in relation to their distance from the ground reference points. This skill is vital for developing a keen sense of spatial orientation and improving overall flight competency.

Other options, such as S-turns, involve flying back and forth between two points but do not require the aircraft to maintain circular paths. Turns about a point focuses on maintaining a constant radius turn around a single reference point, and shallow turns emphasize gradual changes in direction without the added complexity of multiple circular paths. Thus, Eights on Pylons is the correct choice for the specific criteria of flying around two selected points in a circular manner.