A fact from Apollonian gasket appeared on Wikipedia's
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any topic like this just cries out for illustrations so us folks that aren't so hot at math can understand what's being discussed. Suppafly
yeah, this page def needs a pic, or at least a link to one.
The image was added 22:06, 8 Oct 2004 [1], before the second comment (Matt me's) above (06:02, 9 Oct 2004, [2]). Hyacinth 18:11, 9 Oct 2004 (UTC)
I think the page needs the construction image https://commons.m.wikimedia.org/wiki/File:Apollonian_gasket_construction.svg in order to make clear exactly which are the 4th & 5th circles. As a clueless non-editor, I don't dare attempt such a potentially space-disrupting change. Snowsim ( talk) 04:24, 13 August 2015 (UTC)
Article should explain from the start that C1, C2, C3 can be any size
Isn't there a " Descartes circle theorem" or some such, relating circle sizes using integers? A very short google showed articles at mathworld, but no mention of integers ... maybe I'm imagining the bit about integers?? linas 02:16, 11 November 2005 (UTC)
To obtain an integer packing one needs four integer curvatures that satisfy DCE, not just three. The first three in the tables happen to produce the fourth, but how were these first 3 obtained to begin with? Are all possible packings accounted for? Also, DCE solutions [2,3,6,23] yield the same packing as [-1,2,2,3]. How does one move from the one characterization to the other? This could be explained a little better. Otherwise, very nice article. —Preceding unsigned comment added by 67.253.170.147 ( talk) 15:17, 1 July 2010 (UTC)
Hi. Can apollonian gaskets be divided in types like :
? -- Adam majewski ( talk) 18:37, 17 July 2010 (UTC)
I created an interactive JavaScript demo at http://www.jasondavies.com/apollonian-gasket/ but I couldn't add the link to the External Links section due to potential conflict of interest. Can someone review it and add if appropriate? Thanks! Jason Davies ( talk) 13:42, 16 August 2010 (UTC)
|very nice effort! 124.170.34.249 ( talk) 02:14, 6 August 2014 (UTC)
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I'm surprised not to see a picture of the special case (0,0,1,1), and it's relationship to Ford Circles. Is there any objection to adding one, for example, as in figure 2 of this article http://www.math.ucsd.edu/~ronspubs/03_02_appolonian.pdf ? The figure shown in the article is similar to the one shown on the Ford Circle page, but has more circles and is, I think, more clear. If there are no objections, I will (eventually) create the picture and add a description somewhere in the section on integral packings. Nilesj ( talk) 19:53, 22 January 2018 (UTC)
"(in the general construction, these three circles have to be different sizes, and they must have a common tangent)" I'm not an expert, but shouldn't that be "three circles may be different sizes" ? Chris2crawford ( talk) 13:41, 3 December 2020 (UTC)
I'd love to see this article worked in with a nicely-explained example: The Local-Global Conjecture for Apollonian circle packings is false
https://www.quantamagazine.org/two-students-unravel-a-widely-believed-math-conjecture-20230810/ ★NealMcB★ ( talk) 20:53, 12 August 2023 (UTC)
A fact from Apollonian gasket appeared on Wikipedia's
Main Page in the
Did you know column on 11 October 2004. The text of the entry was as follows:
|
This article is rated B-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||
|
any topic like this just cries out for illustrations so us folks that aren't so hot at math can understand what's being discussed. Suppafly
yeah, this page def needs a pic, or at least a link to one.
The image was added 22:06, 8 Oct 2004 [1], before the second comment (Matt me's) above (06:02, 9 Oct 2004, [2]). Hyacinth 18:11, 9 Oct 2004 (UTC)
I think the page needs the construction image https://commons.m.wikimedia.org/wiki/File:Apollonian_gasket_construction.svg in order to make clear exactly which are the 4th & 5th circles. As a clueless non-editor, I don't dare attempt such a potentially space-disrupting change. Snowsim ( talk) 04:24, 13 August 2015 (UTC)
Article should explain from the start that C1, C2, C3 can be any size
Isn't there a " Descartes circle theorem" or some such, relating circle sizes using integers? A very short google showed articles at mathworld, but no mention of integers ... maybe I'm imagining the bit about integers?? linas 02:16, 11 November 2005 (UTC)
To obtain an integer packing one needs four integer curvatures that satisfy DCE, not just three. The first three in the tables happen to produce the fourth, but how were these first 3 obtained to begin with? Are all possible packings accounted for? Also, DCE solutions [2,3,6,23] yield the same packing as [-1,2,2,3]. How does one move from the one characterization to the other? This could be explained a little better. Otherwise, very nice article. —Preceding unsigned comment added by 67.253.170.147 ( talk) 15:17, 1 July 2010 (UTC)
Hi. Can apollonian gaskets be divided in types like :
? -- Adam majewski ( talk) 18:37, 17 July 2010 (UTC)
I created an interactive JavaScript demo at http://www.jasondavies.com/apollonian-gasket/ but I couldn't add the link to the External Links section due to potential conflict of interest. Can someone review it and add if appropriate? Thanks! Jason Davies ( talk) 13:42, 16 August 2010 (UTC)
|very nice effort! 124.170.34.249 ( talk) 02:14, 6 August 2014 (UTC)
Hello fellow Wikipedians,
I have just modified 2 external links on Apollonian gasket. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{
Sourcecheck}}
).
This message was posted before February 2018.
After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than
regular verification using the archive tool instructions below. Editors
have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
RfC before doing mass systematic removals. This message is updated dynamically through the template {{
source check}}
(last update: 18 January 2022).
Cheers.— InternetArchiveBot ( Report bug) 12:38, 16 October 2016 (UTC)
I'm surprised not to see a picture of the special case (0,0,1,1), and it's relationship to Ford Circles. Is there any objection to adding one, for example, as in figure 2 of this article http://www.math.ucsd.edu/~ronspubs/03_02_appolonian.pdf ? The figure shown in the article is similar to the one shown on the Ford Circle page, but has more circles and is, I think, more clear. If there are no objections, I will (eventually) create the picture and add a description somewhere in the section on integral packings. Nilesj ( talk) 19:53, 22 January 2018 (UTC)
"(in the general construction, these three circles have to be different sizes, and they must have a common tangent)" I'm not an expert, but shouldn't that be "three circles may be different sizes" ? Chris2crawford ( talk) 13:41, 3 December 2020 (UTC)
I'd love to see this article worked in with a nicely-explained example: The Local-Global Conjecture for Apollonian circle packings is false
https://www.quantamagazine.org/two-students-unravel-a-widely-believed-math-conjecture-20230810/ ★NealMcB★ ( talk) 20:53, 12 August 2023 (UTC)