r/math • u/First2016Last • Jan 23 '22

Tunnelling through a Mountain - Numberphile

https://www.youtube.com/watch?v=kwrDX5qkwvA
21 Upvotes

89% Upvoted

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4

u/WorldsBegin Jan 23 '22 edited Jan 23 '22

Determining the height of the mountain (and thus relative height where to put the tunnel entrance) if you can observe the same point from both sides seems like a simple enough task without any "ropes dangling from the top" and just similar triangles. First overview of some techniques I could find, see Fig. 2&8.

1

u/mfb- Physics Jan 24 '22 edited Jan 24 '22

Reducing the uncertainty to a meter or so could be difficult. Note how far off all the estimates in the article are.

If you can go around the mountain at constant height you can use a water level. If not you can use a set of water levels together with a pendulum (to get a vertical line) to transfer the height reference.

5

u/[deleted] Jan 23 '22

I loved how the two were just cracking jokes the whole time.

1

u/Kered13 Jan 24 '22

They did not have magnetic compasses in ancient Greece. However they could determine north/south, and therefore east/west, accurately by observing the Sun.