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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: |
| 22-Aug-2022 | 05-Jun-2024 | 25-Jun-2013 | 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) | Circles in a circle (ri = i-1/5) | Circles in a circle (benchmark instances) | Packomania's wizard |
| Last updated: | Last updated: | Last updated: | Last updated: | Last updated: | Last updated: | Revived: |
| 01-Jun-2024 | 01-Jun-2024 | 02-Jun-2024 | 01-Jun-2024 | 01-Jun-2024 | 02-Jun-2024 | 07-Feb-2022
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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: |
| 28-Oct-2015 | 08-Oct-2015 | 08-May-2013
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Thanks to Neil J. A. Sloane and Ya-Ping Lu who triggered me to resume the work.
| Circles in a regular pentagon | Circles in a regular hexagon | Circles in a regular heptagon | Circles in a regular octagon | Circles in a regular nonagon | Circles in a regular decagon | Circles in a regular hendecagon | Circles in a regular dodecagon | Circles in a regular tridecagon | Circles in a regular tetradecagon | Circles in a regular pentadecagon | Circles in a regular hexadecagon | Circles in a regular heptadecagon |
| Last updated: | Last updated: | Last updated: | Last updated: | Last updated: | Last updated: | Last updated: | Last updated: | Last updated: | Last updated: | Last updated: | Last updated: | Last updated: |
| 06-Mar-2023 | 18-Dec-2020 | 05-Dec-2020 | 05-Dec-2020 | 05-Dec-2020 | 05-Dec-2020 | 07-Dec-2020 | 07-Dec-2020 | 07-Dec-2020 | 08-Dec-2020 | 14-Dec-2020 | 07-Mar-2023 | 10-Dec-2020
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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 equal spheres in fixed-sized containers with maximum packing density
| Spheres in a cube | Spheres in a sphere |
| Last updated: | Last updated: |
| 29-Jun-2018 | 26-Sep-2024 |
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Section 4: Literature
Literature