The only constructable primes are 2 and the Fermat primes, probably just 3, 5, 17, 257, 65537. It doesn't seem like any explicit geometric construction was used for this device, probably just measuring out the circumference and tooling the gaps as appropriate. They did have techniques (mechanical linkages, I think, and certainly neusis) which allowed the construction of many more, though in neither case is 223 constructable. Charles Greathouse Analyst/Programmer Case Western Reserve University On Fri, Nov 30, 2012 at 2:42 PM, Henry Baker <hbaker1@pipeline.com> 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 ?
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