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] --
Nice! On Jul 26, 2015 11:11 AM, "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.
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On 2015-07-26 11:11, Tom Rokicki 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.
Works (wow) in Firefox, except it introduces typos: "and this page computers the locations"-) --rwg
Neat! Yes, both IE and Firefox work fine. But you have a typo: "computers" should be "computes". Also, If you want to use quotes instead of italic or bold, you should use real quotes (“ and ”) rather than the annoying " --ms On 26-Jul-15 14:11, Tom Rokicki 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.
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.
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(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.
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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.
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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.
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<< 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. 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] --
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I would be interested to turn some of these into animated gifs. Any suggestions for how to do that? On Sun, Jul 26, 2015 at 9:34 PM, 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.
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.
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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.
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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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I broke it, by setting a = -1 ... [ Which may seem a perverse thing to do, and lacking mechanical meaning. However my first attempt at a program represented gears by anti-tangent "oriented circles" (Moebius half-spaces), bestowing negative radius upon yer common-or-garden sun. ] WFL On 7/29/15, Fred Lunnon <fred.lunnon@gmail.com> wrote:
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 > > > _______________________________________________ > math-fun mailing list > math-fun@mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (7)
-
Fred Lunnon -
James Buddenhagen -
Mike Beeler -
Mike Speciner -
rwg -
Tom Rokicki -
William R. Somsky