On 11/30/2012 11:42 AM, Henry Baker wrote:
At 08:48 AM 11/25/2012, Robert Baillie wrote:
here is an interesting (58 minute) bbc documentary that explains in more detail how the device actually works, as far as we know today: http://www.youtube.com/watch?v=-rUsgL2VGeU
many of the gears had a prime number of teeth. this was very helpful in figuring out what the device was used for, and how it worked. Fabulous video; highly recommended!!
Ok, all you algebra geeks: these gears with prime numbers of teeth had to be built, so which of the prime numbers in this device are "constructible" using a straight-edge and compass ?
For the non-constructible numbers, how did the Greeks construct them? Which additional operations were allowed to enable the construction of those gear wheels ?
The way uniform machines were first constructed was by using symmetry. Polishing three metal blocks against one another produces a plane surface. If you run two chased screws against one another you get a uniform helical pitch. I imagine the Greeks did the same. If you rough out the teeth on two gears that are relatively prime and then run them against one another with some abrasive compound you get uniform spacing. Brent