A curved chase with four participants and a symmetry that is not broken at any time.

The four turtles

Reasoner
Timeless ingenuity

Riddle statement

Four turtles occupy the four corners of a square of 10 centimeters on each side.

They all start to move at the same time and at the same speed.
Each one always advances in the direction of the turtle in front of it, continually turning to aim at it.

How far does each turtle travel before the four turtles meet?