Another limitation, which should be easily rectifiable, is that the sun is prevented from overlapping the ring. The trivial extreme train has sun externally tangent to ring, and planets internally tangent at the same point; though including that in the demo would probably require a separate special case, and may not be worth the trouble. WFL On 7/27/15, Fred Lunnon <fred.lunnon@gmail.com> wrote:
On 7/27/15, Fred Lunnon <fred.lunnon@gmail.com> wrote:
<< My solution method will not work for two pairs of equal planets >> which would anyway in general imply sun and ring concentric and planet centres undefined. ["Somsky" pairs meant above, ie. (teeth on) planets + sun = ring.]
The demo lacks one feature I should like to see: instead of (curiously) insisting on the smaller planet of a pair being specified, why not allow the user to enter that planet to be placed to the left of the axis?
WFL
On 7/27/15, Tom Rokicki <rokicki@gmail.com> wrote:
Thanks, Fred!
I should be able to fix the case of one pair of equal planets. My solution method will not work for two pairs of equal planets, but it should permit one pair. I'll have to fix that.
And I should extend it to support more than two planet pairs as well . . .
I want to correct a statement I made; I said the vector sum of the vectors from the center of the outer gear to the center of the constituent gears of a Somsky set sums to zero; that's not right. The sum of the vectors from the center of the outer gear to the center of the two planet gears is equal to the vector from the center of the outer gear to the sun gear.
-tom
On Sun, Jul 26, 2015 at 5:47 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Runs under Opera as well.
The solver doesn't seem able to cope with diametrically opposite pairs of equal planets --- eg. a subset of Somsky's 8-planet set d,a,b,c = 53,27,13,3 Also the error message has lost a right parenthesis: (it must be at most 12
WFL
On 7/26/15, Tom Rokicki <rokicki@gmail.com> wrote:
(blush).
You'll notice that the vector sum of the three Somsky gears (the sun and a pair of planets) always sum to zero. This is clear on the Somsky proof (from the central parallelogram).
There are certain input values for which the offset is rational; I believe these correlate with pythagorean triples. This also correlates with the existence of solutions with more than one pair of planets. There are some avenues of exploration open here.
On Sun, Jul 26, 2015 at 1:01 PM, Mike Beeler <mikebeeler@verizon.net> wrote:
Wonderful, thank you! Not since Bill Gosper’s animation of Steiner’s porism on the PDP-6 have I enjoyed circles in motion so much! The good old days are not gone, just transmuted — and now they have teeth! :-)
— Mike Beeler
> On Jul 26, 2015, at 2:11 PM, Tom Rokicki <rokicki@gmail.com> wrote: > > This page lets you play with meshing Somsky gears. > > http://tomas.rokicki.com/somsky.html > > I've tested it on Chrome and Safari; if someone lets me > know if it works on firefox or IE, I'd appreciate it. > > -- > -- http://cube20.org/ -- [Golly link suppressed; ask me why] -- > > _______________________________________________ > math-fun mailing list > math-fun@mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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