This makes ancient tunnels fascinating subjects for study.
The Tunnel of Eupalinos, on the Greek island of Samos, is one such example.
The tunnel was dug from both ends and met beneath Mount Kastros highest point.
This way, Eupalinos had only to ensure the shafts were dug at the same level.
As long as the two digging teams maintained level, the two shafts would eventually cross each other.
Eupalinos was aware that failing to meet would be catastrophic.
So he had the shafts dug in a zigzag fashion near the meeting point.
They would have changed direction as needed, coordinating their digging effort until they met.
The sharp turns near the meeting point attest to this theory.
The precision was so outstanding that at the meeting point the vertical offset was only 60 centimeters.
EuclidsElements, the first major compendium of ancient mathematics, was written some 200 years later.
Another famous example is the considerably longer Channel Tunnel that was completed in 1994.
Even with the full power of modern technology, Channel Tunnel didnt meet exactly in the middle.
By comparison, Eupalinos used very little mathematics.
How he managed to pull off one of the finest engineering achievements of ancient times is a mystery.
Sketch of the tunnels cross section, adapted from the original by Tom M. Apostol.
The tunnel itself is 1,036 meters long, and about 2 meters wide and 2 meters high.
Vertical shafts link this channel to the main tunnel roughly every ten meters.
Within the channel, water was transported in an open-top terracotta drain.
