The Tunnel of Samos

[Leviset]

Don’t know how many of you already know about this, but I find it an amazing engineering and mathematical project constructed way before calculators or even serious mathematics?
Dennis
https://fermatslibrary.com/s/the-tunnel-...newsletter
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[Terje Vallestad]

(01-22-2019 04:32 PM)Leviset Wrote:  Don’t know how many of you already know about this, but I find it an amazing engineering and mathematical project constructed way before calculators or even serious mathematics?
Dennis
https://fermatslibrary.com/s/the-tunnel-...newsletter
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A very interesting read
Thanks for sharing

Cheers, Terje

[Massimo Gnerucci]

Since when 1036 meters = 4000 feet?

[pier4r]

Thanks for sharing.

For the conversion feet to meter, maybe the measurement used in the samo island was different from the 302mm average found in ancient Greek sources or ruins.

https://en.wikipedia.org/wiki/Foot_(unit)

[BruceH]

It's an interesting article but I'm confused by the bit that suggests determining a right-angle was difficult to do precisely, suggesting the Hero would have used a dioptra.

Surely three straight pieces of wood, length 3, 4 and 5 units, pinned through holes at the ends (the holes being 3, 4, and 5 units apart) would create a right-angle?

And if there is too much flex in the thing, then a double-length base and two triangles would ensure that the right angle was fairly rigid. Or make it bigger. Or both!

[pier4r]

well try a bit. I think it is fairly easy to get some inaccuracies that if repeated a couple of times, are no problem, but on long distances may create problems.

[Leviset]

I think the article mentions that probably not enough mathematics was known to be able in the 6th century BC to tackle the tunnel build, Pythagoras was born in 569BC

[BruceH]

True. I hadn't twigged that Hero's method was proposed so long after the tunnel was built.

It's possible that they used some other method entirely, given that the article says that the tunnel does actually bend a bit in the middle yet, clearly, they managed to make both ends meet.

[pier4r]

(02-02-2019 11:42 PM)Leviset Wrote:  I think the article mentions that probably not enough mathematics was known to be able in the 6th century BC to tackle the tunnel build, Pythagoras was born in 569BC

The pythagorean theorem was somewhat known already. I mean, in the past - but even today - it is most likely that things were rediscovered over and over unless very deep.

http://www-history.mcs.st-and.ac.uk/Hist...goras.html
Wiki has useful pointers. https://en.wikipedia.org/wiki/Pythagorean_theorem