Re:The Calculus They Won't Teach You [video]
by not2b on Wednesday January 04, 2023 @12:15PM
(#34248394)
Erastosthenes did it by comparing the angle of the shadow cast by a stick on the summer solstice at noon in two cities, Alexandria and Syene (now Aswan), which are about 800 km apart. What was special about Syene was that it is so close to the Tropic of Cancer line that the sun would hit the bottoms of wells on the solstice, meaning that he only needed one stick, in Alexandria, and the distance between the cities, to do his estimate. His error was about 2%.
He's also famous for the sieve of Erastosthenes for finding prime numbers and figuring out the earth's axial tilt.
Re:The Calculus They Won't Teach You [video]
by a9h74j on Wednesday January 04, 2023 @04:56PM
(#34252426)
Darn, at some point I started imagining he had a protocol for synchronizing clocks over a distance. assuming the difference was in longitude. (E.g. Symmetric NTP over carrier pidgeon.)
Re:The Calculus They Won't Teach You [video]
by not2b on Wednesday January 04, 2023 @05:56PM
(#34253164)
Longitude was a much tougher problem to solve.
Re:The Calculus They Won't Teach You [video]
by a9h74j on Thursday January 05, 2023 @02:05AM
(#34256943)
Yea, recalling the book of that name might have contributed to my drift of recollection. Solvable earlier on land (but not sea) on terms of clock synchronization.
Re:The Calculus They Won't Teach You [video]
by amluto on Wednesday January 04, 2023 @05:48PM
(#34253071)
You can get a vaguely credible estimate by standing on a (small!) hill and measuring the distance to the horizon. Works better if you have a body of water handy, because bodies of water are nice and flat.
The history is useful there, I think. First off, it is motivating — that’s a pretty big question, really shows what math can accomplish without much hardware. Second, it provides some sort of useful constraints if you are trying to work out the computation yourself. In a textbook the problems are always a bit artificial, some info will be given, some hidden. “Anything an Ancient Greek would have” is a bit more real-world, you can see where the constraints come from.