A sequence, let it rotate for the nth time, and the path A has traveled is an (note that it is the nth time).

Then 1 th rotation, a 1=2*pai/(3)

Second rotation, a2=2*pai/(3)

The third rotation, because at this time, centered on A, a3=0.

4th rotation, a4=2*pai/(3)

Therefore, after four turns, the total distance traveled by A is S4=a 1+a2+a3+a4=2*pai.

Analysis, when taking A as the center, this rotation A has not traveled any distance, but taking non-A point as the center, A has traveled the same distance, which is the arc length formula (θ* R, θ is the rotation angle of 120 degrees). Therefore, if four times are taken as a cycle, the total driving distance is 2*pai.

Then after 25 times, S=6*2*pai+2*pai/(3)=38*pai/3.

Hope to adopt!