In a scene in Seven Years in Tibet, Heinrich and Peter make a bet over their calculations of the distance to Tibet. They are quite precise – 65 vs 68 kilometres. They don’t have any devices, not even a map. Just pencil and a notebook. When they reach the border, Heinrich says he wins the bet as it’s exactly 68 km, and Peter seems to agree. How did they measure it?
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So, their’s a few methods that all boil down to estimates and heuristics, such as step counting, travel time calculations, and so on. Other methods could include high accuracy measurements of certain astronomical events, like the change in noon or the exact time a specific star rose, etc, but these all require clocks accurate to the second over extended periods of time, which historically were quite bulky.
Their’s also a much more rigours approach involved triangulation and trigonometry, but from the context you have given, I’d assume that’s not the case.
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