It can be proved that the trajectory is round.
As shown in the figure, P is the moving point on the circle O, A is the fixed point, connecting AP, and Q is the midpoint of AP. When point P moves on circle O, find the trajectory of point Q, connect OA and OP, take the midpoint of OA and connect QM, then QM=OP, and the trajectory of point Q is a circle with m as the center.
The Application of Cucurbita Principle in Mathematics
The principle of melon and bean can be strictly proved mathematically. If there is no strict proof, it can also be explained by holistic thinking and equivalent thinking. The first is the dialectical relationship between the individual and the whole. The whole is composed of multiple individuals, such as a straight line or a circle composed of multiple points. In the melon-bean problem, a single moving point is an individual, and the trajectory (straight line/line segment, circle, polygon) is a whole.
To understand the principle of melon and bean, we should use holistic thinking, from the linkage correspondence between driving point and driven point to the correspondence and linkage of their motion trajectories. Correspondence: the trajectory of the driving point corresponds to the trajectory of the driven point, such as straight line to straight line and circle to circle; Linkage: the trajectory of the active point is translated &; Spin and potential conversion, the change produces the trajectory of the driving point.