Timeline for How can the centers of these 5 related circles be specified as a formula?
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| Apr 28, 2015 at 22:39 | history | edited | VividD |
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| Mar 24, 2015 at 16:16 | audit | Close votes | |||
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| Mar 15, 2015 at 10:23 | audit | Close votes | |||
| Mar 15, 2015 at 11:34 | |||||
| Mar 14, 2015 at 3:00 | comment | added | David K | FYI, OpenOffice can install a free extension for Calc called Solver for Non-Linear Programming. As I recall it's not hard to use (though you still have to set up the formulas that you want to optmize). In any case if you use Excel you probably should have OpenOffice Calc too in any case. | |
| Mar 13, 2015 at 21:37 | answer | added | GEdgar | timeline score: 1 | |
| Mar 13, 2015 at 18:34 | answer | added | Victor Liu | timeline score: 2 | |
| Mar 13, 2015 at 14:42 | comment | added | David | Hi Ross Millikan, I think you missed one key point. In the case where I discuss leaving out Blue Green and Yellow, I also mention that the tops of the Orange and Purple would then be required to be at the same height, that is, they would be the ones which would then be tangent to the top of the bounding rectangle, which obviously would be shorter. That would mean that there is only one solution and it's a pretty simple one. Thanks for playing though! | |
| Mar 13, 2015 at 14:28 | comment | added | David | Thanks David K. As I mentioned above, the Excel approach got me close enough for most practical purposes, but it's off just a bit as can be seen in the picture. Note that the horizontal line between the Yellow and Orange circles isn't quite straight in the picture. Technically it should be at 90 degrees to the outer rectangle. So should the similar lines between Blue and Purple as well as between Purple and Red. The reason it's off in the drawing is because I couldn't get any closer with Excel, and I had to manually translate the Excel numbers into the drawing program too. | |
| Mar 13, 2015 at 14:22 | comment | added | Ross Millikan | Without the blue, green, and yellow circles you don't have enough information for a solution. The purple could grow some and the orange shrink appropriately to keep the three circles tangent and the centers on the vertical lines. | |
| Mar 13, 2015 at 14:16 | history | edited | David | CC BY-SA 3.0 |
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| Mar 13, 2015 at 14:03 | comment | added | David K | It sounds like what you have done in Excel is a numeric-methods solution to the problem, with a considerable amount of manual effort included to overcome the lack of a general solver in Excel. I'd consider that a legitimate approach. I am interested to see if there is a more "clever" way to do it. | |
| Mar 13, 2015 at 14:02 | comment | added | GEdgar | added picture... | |
| Mar 13, 2015 at 14:02 | history | edited | GEdgar | CC BY-SA 3.0 |
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| Mar 13, 2015 at 14:00 | answer | added | bubba | timeline score: 3 | |
| Mar 13, 2015 at 13:57 | history | edited | David | CC BY-SA 3.0 |
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| Mar 13, 2015 at 13:51 | history | edited | David | CC BY-SA 3.0 |
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| Mar 13, 2015 at 13:46 | history | edited | David | CC BY-SA 3.0 |
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| Mar 13, 2015 at 13:14 | comment | added | Panglossian Oporopolist | Welcome to MSE sir! Can I say your question is extremely interesting? Good job! I don't have an answer as of yet, will try a while later when free (I've my exams going on..). Do expect solutions from someone or the other to follow, for this site has no lack of geniuses. Also, you've posted it to the right place indeed... Have fun on this community! | |
| Mar 13, 2015 at 12:38 | review | First posts | |||
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| Mar 13, 2015 at 12:32 | history | asked | David | CC BY-SA 3.0 |