20200213, 13:02  #12  
Nov 2003
16444_{8} Posts 
Quote:
method is very quickly pushed to its limits. 

20200213, 16:55  #13  
Feb 2017
Nowhere
3,319 Posts 
Quote:
If you want to see currently stateoftheart methods being pushed to their limits, you could do worse than some of the threads of the Mersenne Forum. 

20200213, 17:45  #14  
Nov 2003
2^{2}·5·373 Posts 
Quote:
They built a number of them. A papertape sieve, the photo electric gear sieve, DLS127, DLS157, etc. Back in the 80's when the computer museum was still in Boston I got to play with their photoelectric sieve. It was not on display (of course!). It was held in storage because the public would never be interested in such a thing (can you hear the sarcasm?). It lacked a drive belt, light source, and photo receptor, but I provided a common auto fan belt that fit, a gas laser and a photo multiplier and got it to work. [I had a letter from Dick Lehmer to the museum staff asking the staff to let me try]. I was actually amazed that the drive motor still functioned. The device had a bunch of gears, each with a prime number of teeth. Each gear also had a circular ring of small holes, corresponding to the teeth. You programmed the thing by plugging the holes with toothpicks! When it was turned on it would spin all the gears until one set of holes lined up. The lineup was detected by a flash of light that poked through the holes. A counter on the top revealed the number of revolutions. It was clunky and slow relative to even a Sun2, but it worked! I had fun trying to explain the thing to the staff. They were clueless as to what the machine was or even after I explained it. The sad thing is that the device was on display at least back in 1984 when the museum was still at DEC in Marlborough. I know, because I was working there at the time. [an extraordinary coincidence, which is how I knew about the status of the machine]. 

20200213, 19:45  #15  
Feb 2017
Nowhere
3,319 Posts 
Quote:
There's a photograph of it in the book to which I provided a link. If you go there, a text search for "gears" will get you to the right place pretty quickly. 

20200218, 20:29  #16  
Apr 2012
2^{4}×3×7 Posts 
Quote:
Last fiddled with by jwaltos on 20200218 at 20:42 

20200225, 18:01  #17  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
1058_{16} Posts 
Quote:
Thinking back to my engineering career, I recalled prime tooth count being unusual. Although it is sometimes put to good use. https://engineering.stackexchange.co...rsinpractice Going through an old Stock Drive Products/Sterling Instrument catalog, I found the following prime tooth counts available, in at least one pitch and pressure angle: 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 59, 71, 109, 127. That's in about 200 pages of catalog. Last fiddled with by kriesel on 20200225 at 18:36 

20200225, 18:14  #18  
Nov 2003
2^{2}·5·373 Posts 
Quote:
BTW. The computer museum moved to California. I do not know what became of the machine. Last fiddled with by R.D. Silverman on 20200225 at 18:15 

20200226, 00:43  #19 
"Mike"
Aug 2002
16625_{8} Posts 
On our racing bicycle we use an odd and an even pair of gears if possible. This distributes the wear better. Our gearing is 53/44 front and 11121314151617181921 rear. (We don't use the 53 much!)
So 11, 13, 17, 19 and 53 are prime. PS  Interesting stuff: https://en.wikipedia.org/wiki/Involute_gear 
20200226, 19:48  #20 
Bamboozled!
May 2003
Down not across
10,151 Posts 
My copy of Sidgewick's Amateur Astronomer's Handbook in La Palma so unavailable for consultation. I know he gave a list of possible gear ratios to change mean solar time to sidereal time for driving an equatorial mount. There are 366.2425 sidereal days per annum but only 365.2425 solar days.
IIRC, the best two sets had errors down in the ppm range. 
20200308, 20:05  #21  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
1000001011000_{2} Posts 
Quote:
The solar day/solar year figure I recall from designing a solar tracking drive in the 1970s was 365.24202.. (probably measurement error bigger back then or remembering wrong). As I recall from a guest speaker in a high school math class, the method of continued fractions is good for arriving at whatever level of approximation you'd like by rational numbers. The 365.2425 number you gave looks to be the Gregorian calendar approximation. 365 most years +.25 from years divisible by 4 having a leap day .01 from excluding years divisible by 100 +.0025 from years divisible by 400 being leap years. 365.2425 total. 

20200308, 20:55  #22  
Bamboozled!
May 2003
Down not across
10,151 Posts 
Quote:
Wikipedia doesn't need fixing. It quotes a sidereal year in units of solar days. A sidereal day is indeed shorter than a solar day by (close to) the ratio I gave. If it helps, recall that the Earth rotates once with respect to the stars as it goes around the sun in its orbit in addition to the rotations it makes on its axis. That is where the 366/365 approximation comes from. Last fiddled with by xilman on 20200308 at 21:02 

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