3 ms·

Wasn't he a bit lucky here? Those two cities are almost directly above each other in the north-south direction. If they had been differently located, it sounds

Wasn't he a bit lucky here? Those two cities are almost directly above each other in the north-south direction. If they had been differently located, it sounds like the measurement would have way off?

jibbit 5y ago
is it just me or is that a poor description of how he did it? I certainly couldn't recreate it. Your comment gives me an important bit of info i was missing.
uranusjr 5y ago
The story presented in the article is actually a simplified example presented by Cleomedes to explain the method. It is unknown what Eratosthenes did to derive the calculation, but according to Eratosthenes, he used existing surveyed measurements to derive the value, likely with the understanding of the relative locations of those measurements beforehand.
todd8 5y ago
No, it doesn't matter which direction the cities are from each other. The calculations assume that the earth is spherical so the calculations work because a great circle will pass between the cities even if they lie at the same latitude. The calculations also assume that the well and the pole lie on a radius of the earth, that is, that they are straight up and down; this can be determined with a simple plumb line. The calculations also assume that the shadow cast by the pole lies on the line between the two cities, but this is always true if the well is pointing straight at the sun. Note that the well in the first city is pointing straight at the sun at a particular time (noon on the summer solstice). Why is this time important? Because it can be accurately determined in the second city without clocks, with accurate clocks (or communication to synchronize the observations) this measurement could be made between any cities at any time as long as the sun was shining straight down the well of one of the cities at that time.

3 ms·

Wasn't he a bit lucky here? Those two cities are almost directly above each other in the north-south direction. If they had been differently located, it sounds

by petters 5y ago

jibbit 5y ago
is it just me or is that a poor description of how he did it? I certainly couldn't recreate it. Your comment gives me an important bit of info i was missing.
uranusjr 5y ago
The story presented in the article is actually a simplified example presented by Cleomedes to explain the method. It is unknown what Eratosthenes did to derive the calculation, but according to Eratosthenes, he used existing surveyed measurements to derive the value, likely with the understanding of the relative locations of those measurements beforehand.
todd8 5y ago
No, it doesn't matter which direction the cities are from each other. The calculations assume that the earth is spherical so the calculations work because a great circle will pass between the cities even if they lie at the same latitude. The calculations also assume that the well and the pole lie on a radius of the earth, that is, that they are straight up and down; this can be determined with a simple plumb line. The calculations also assume that the shadow cast by the pole lies on the line between the two cities, but this is always true if the well is pointing straight at the sun. Note that the well in the first city is pointing straight at the sun at a particular time (noon on the summer solstice). Why is this time important? Because it can be accurately determined in the second city without clocks, with accurate clocks (or communication to synchronize the observations) this measurement could be made between any cities at any time as long as the sun was shining straight down the well of one of the cities at that time.