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2 3 4 5 6 7 8 9 10 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 discs shortfall of the symmetric search 14.6% 1.7% 0.0% -0.0% 5.6% 0.5% 10.8% 10.4% 4.7% symmetry: mirror · both searches at 90 restarts neither number is a proved optimum — this compares two searches
Symmetry
1
When symmetry costs
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The shapes the optimum has
3
The symmetry the letters cannot keep
4
The symmetry a gluing adds
4 essays · design
found rather than designed crushed drink cans, tree bark, deployable booms at every interior vertex sectors 60°, 60°, 60°, 60°, 60°, 60° two courses and four diagonals two of one letter, four of the other why the height is not free a steeper diagonal makes the top sector strictly smallest, flanked by two of the same letter 20 interior vertices · 23 mountain and 56 valley creases mountain valley raw edge
Found patterns
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Patterns nobody designed
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The cylinder the pattern chooses
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The period nobody measured
3 essays · tessellation
4 patterns, one folded profile 1/12 2/12 4/12 7/12 2 5 3 1 1/12 3/12 6/12 8/12 2 5 3 1 2/12 4/12 5/12 7/12 2 5 3 1 2/12 5/12 7/12 8/12 2 5 3 1 folded the layer counts under each band are the same in every row, and so are the widths
Inverse problem
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The shadow does not name the pattern
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The order does not name it either
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Which side is showing
3 essays · flat-folding
interior vertices, by number of creases meeting there none 3 odd 59 4 even none 5 odd 32 6 even none 7 odd 1 8 even 8 patterns, 92 interior vertices, and not one of them with an odd number of creases
Vertex degree
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Nothing meets at three
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Six creases and the same straight line
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A knife edge nine decimals wide
3 essays · flat-folding
the waterbomb tessellation's odd vertex degree six, and this site prints nine of them on one sheet every assignment 64 passes all four conditions 30 has a flat folded state 18 12 labellings satisfy every condition the subject has and have no flat folded state
Crimping
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Crimp it away and ask again
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A tie is not a decision
2 essays · flat-folding
the pattern the panels, folded sheet 12.000 footprint 1.966 · 6.11 layers on average · 12 at the deepest 1.966 × 6.11 = 12.007, which is the sheet
Conservation
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The paper is all still there
1 essay · flat-folding
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