How do you dig a tunnel through a mountain when you don’t have access to any modern equipment? This was the challenge on a Greek island called Samos during the 6th century BCE, around 2,500 years ago.

The Samians wanted to create an aqueduct through Mount Kastro, a distance of 1,036 meters (3,399 feet). They achieved this ancient engineering marvel by digging by hand plus some geometry.

In this Numberphile video, mathematician Professor Hannah Fry introduces the math that built Tunnel of Eupalinos, now a tourist site and part of the UNESCO World Heritage Site, the Pythagoreion.

The aqueduct, a remarkable example of how mathematics can be used to solve complex engineering problems, was the second-known tunnel to be excavated from both ends and the first known to use geometry to do it. She explains:

“You need a technique to make sure that these two lines end up meeting up in the middle. And the way that you do that is by using triangles…”

“So you try and walk around from one side of the mountain to the other, and as you go… every time you take a step south you add it up, every time you take a step to the west you add up, and you’re very careful about how big all of your steps are as you’re going…. in total then, imagine that you have taken 84 steps west and you have taken 13 steps south.

“So effectively then, to get the direction from one place to the other, you are talking about a triangle with those [measurements] as the sides.”

Throughout the video, Numberphile’s Brady Haran asks questions that help dispel common assumptions about the challenge while short animations illustrate the engineering. A sponsor message starts around 7 minutes.

Bonus: Measuring the Berlin TV Tower with a ruler.

How could you tunnel through a mountain 2,500 years ago?

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