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*** This page is dedicated to the Hungarian mathematicians who are the pioneers in this discipline. ***
Section 1: Packings of equal and unequal circles in fixed-sized containers with maximum packing density
| Circles in a square | Circles in a circle | Circles in rectangles | Circles in an isosceles right triangle | Circles in a semicircle | Circles in a circular quadrant |
| Last updated: | Last updated: | Last updated: | Last updated: | Last updated: | Last updated: |
| 21-May-2012 | 21-May-2012 | 19-Mar-2011 | 18-Mar-2011 | 16-Apr-2011 | 04-Jul-2011
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| calculation form | calculation form | calculation form |
| Circles in a circle (ri = i) | Circles in a circle (ri = i+1/2) | Circles in a circle (ri = i-1/2) | Circles in a circle (ri = i-2/3) | Packomania's wizard |
| Last updated: | Last updated: | Last updated: | Last updated: | Last updated: |
| 25-Mar-2013 | 22-Mar-2012 | 22-Mar-2012 | 22-Mar-2012 | 08-Sep-2011
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The probably densest irregular packing ever found by computers and humans, of course, like André Müller: ccin200.
| Circles in a square (ri = i) | Circles in a square (ri = i+1/2) | Circles in a square (ri = i-1/2) |
| Last updated: | Last updated: | Last updated: |
| 21-May-2013 | 14-May-2013 | 08-May-2013
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Section 2: Packings of equal and unequal circles in variable-sized containers with maximum packing density
| Circles in rectangles with variable aspect ratio | Circular open dimension problem (CODP) |
| Last updated: | Last updated: |
| 10-Dec-2011 | 01-Nov-2012 |
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Section 3: Packings of variable-sized circles in fixed-sized containers with maximum total sum of perimeters
| Circles in a square |
| Last updated: |
| 19-Jul-2012 |
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Section 4: Packings of equal spheres in fixed-sized containers with maximum packing density
| Spheres in a cube |
| Last updated: |
| 02-Nov-2012 |
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