I heard a talk some months back, from one of the investigators of the Antikythera mechanism. Really fascinating. Discovered over 100 years ago, it's just recently that they finally reverse engineered it, completely. Or so the speaker claimed.
Apparently it was a long development, lasting almost a century, ~ 200 B.C. There's a suspicion that Archimedes had a hand in, but no smoking gun.
It's an astronomical calendar, an astonishing achievement. It could predict solar and lunar eclipses decades ahead!
An interesting point: we have no user manual which specifies the device as a celestial calendar. But the fact is, it makes an amazingly good calendar! Hence, Sherlock, it must be such a device.
In other words, if an unknown object serves a particular function, one may assume it was designed to that purpose, and a designer behind it. With obvious implications for the creation/evolution debate -
Now the technical bit - it consists of a complex interplay of cogwheels; calculators. I recall one had 53 teeth, another 127. How the heck did they construct those? How did they even DRAW them?
Today, with AutoCad, it's a piece of cake. But in the days of Euclid? So, the challenge: armed with only your powerful 21st century brain and education, but B.C. era technology, how would you go about designing and cutting those wheels?