Where Did the Train Stop?

It left at 5:06 AM, destined for a warmer climate.
When it arrived two hours late
There were no passengers on the train.
Where had they gone?

Years later the commission established
To locate the missing 134 people
Issued it's conclusion:
Those missing 134 people left the train.

It seems their group leader
Had convinced them all
That Euclid was right.
Their train could never arrive.

It would halve the distance ever day,
Bringing them closer and closer,
But never quite arriving.
A new plan was needed.

Traveling, without a destination
Would leave them, at the close of each day,
Exactly where they stopped,
They will have arrived.