Here’s one that turned out to be more interesting than John expected. Building a road seems like a pretty easy task, right? But imagine having to do it without proper equipment! Can you think of how to make it work? John sure couldn’t. But long ago in Ancient Rome, a clever proto-engineer figured it out using the power of triangles — and by just lining people up (seriously).
Join us as John learns that trigonometry does, in fact, have real-world uses.
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Additional Technical Background:
Shout out to one of the papers that I used to learn about Roman surveying methods, titled “Designing Roman Roads” by Hugh E. H. Davies.
This first image shows one of the methods they might have used to approximate the distance and bearing of a straight line between two points. This is an example of a basic problem where you might want to dig a tunnel through a mountain (from point D to point B). To do so, you would pace out distances in right angles, getting closer and closer to the other side, then adding up the distances or calculating the hypotenuse to get the total picture of what point D to B looks like. To use the above example, you could get the distance and bearing from P to D by going from P to Q, then D to Q, and finding the hypotenuse. By pacing out the right angles, you can lay out an approximate grid around the mountain that lets you measure the shape of the mountain and then calculate the distances you’d need between points.
Survey lines could be laid out using this exact method, as shown in the second image. Once you have a survey line across two high points, you could also identify features (like a river) based on the survey line. This lets you draw a fairly accurate map of the area you’re trying to build across.
Finally, using multiple survey lines and a rough map of the terrain and area, you could lay out your proposed road alignment. The road alignment can then be relayed back to the survey staff by linking it to the survey lines. To do this, draw lines perpendicular to the survey line to the key points along the road alignment. This way, you can tell the survey staff “go 10 paces along the survey line, then turn 90 degrees and walk 20 paces, that will be one point of the road.” Connect all the points and you’ve got your proposed road laid out on the site!
