The system is a central symmetric system, and the four snails are always on the same circle with the original center as the center. We can set the relationship between the radius of a circle and time as R(t), and we need to find the zero point of R(t), which is the meeting time.
As can be seen from the landlord's picture, the four snails are always arranged in a square, and at any moment, their speed direction is the direction of the inscribed square edge of the circle at that time. The velocity is decomposed into radial and angular directions, and the radial component is the negative two-thirds root sign of the velocity (sine value of -45 degree angle).
So in polar coordinates, there is R(t)= root number two * (1-vt) (when t = 0, the snail's distance center is root number two), where v= 1.
So the snails will meet in the center of the square after 1 second.
In addition, in polar coordinates, the angular velocity is two-thirds root *v, and the angular coordinate a(t) satisfies da=w*dt= two-thirds root * v * dt/r.
, the integral solution is a=-ln( 1-vt), so the trajectory equation without parameter v can be expressed as a=-ln(R* root number two).
So the snail's route has nothing to do with speed.