User:Contribution/Successive superparticular complementary pair: Difference between revisions
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{{todo|Finish the article and move|inline=1|comment=When the article is finished, move it to the main root}} | {{todo|Finish the article and move|inline=1|comment=When the article is finished, move it to the main root}} | ||
{| class="wikitable sortable" | |||
|+ style="font-size: 105%;" | Error (abs, [[Cent|¢]]) on successive superparticular complementary pair in equal divisions | |||
|- | |||
! #ed3/1 !! 2/1, 3/2 error !! #ed2/1 !! 3/2, 4/3 error !! #ed5/3 !! 4/3, 5/4 error !! #ed3/2 !! 5/4, 6/5 error !! #ed7/5 !! 6/5, 7/6 error !! #ed4/3 !! 7/6, 8/7 error !! #ed9/7 !! 8/7, 9/8 error !! #ed5/4 !! 9/8, 10/9 error !! #ed11/9 !! 10/9, 11/10 error !! #ed6/5 !! 11/10, 12/11 error | |||
|- | |||
| [[1ed3/1]] || 701.96 || [[1ed2/1]] || 498.04 || [[1ed5/3]] || 386.31 || [[1ed3/2]] || 315.64 || [[1ed7/5]] || 266.87 || [[1ed4/3]] || 231.17 || [[1ed9/7]] || 203.91 || [[1ed5/4]] || 182.40 || [[1ed11/9]] || 165.00 || [[1ed6/5]] || 150.64 | |||
|- | |||
| [[2ed3/1]] || 249.02 || [[2ed2/1]] || 101.96 || [[2ed5/3]] || 55.87 || [[2ed3/2]] || 35.34 || [[2ed7/5]] || 24.39 || [[2ed4/3]] || 17.85 || [[2ed9/7]] || 13.63 || [[2ed5/4]] || 10.75 || [[2ed11/9]] || 8.70 || [[2ed6/5]] || 7.18 | |||
|- | |||
| [[3ed3/1]] || 67.97 || [[3ed2/1]] || 98.04 || [[3ed5/3]] || 91.53 || [[3ed3/2]] || 81.66 || [[3ed7/5]] || 72.70 || [[3ed4/3]] || 65.16 || [[3ed9/7]] || 58.88 || [[3ed5/4]] || 53.63 || [[3ed11/9]] || 49.20 || [[3ed6/5]] || 45.42 | |||
|- | |||
| [[4ed3/1]] || 226.47 || [[4ed2/1]] || 101.96 || [[4ed5/3]] || 55.87 || [[4ed3/2]] || 35.34 || [[4ed7/5]] || 24.39 || [[4ed4/3]] || 17.85 || [[4ed9/7]] || 13.63 || [[4ed5/4]] || 10.75 || [[4ed11/9]] || 8.70 || [[4ed6/5]] || 7.18 | |||
|- | |||
| [[5ed3/1]] || 58.83 || [[5ed2/1]] || 18.04 || [[5ed5/3]] || 32.57 || [[5ed3/2]] || 34.86 || [[5ed7/5]] || 33.87 || [[5ed4/3]] || 31.96 || [[5ed9/7]] || 29.88 || [[5ed5/4]] || 27.88 || [[5ed11/9]] || 26.04 || [[5ed6/5]] || 24.38 | |||
|- | |||
| [[6ed3/1]] || 67.97 || [[6ed2/1]] || 98.04 || [[6ed5/3]] || 55.87 || [[6ed3/2]] || 35.34 || [[6ed7/5]] || 24.39 || [[6ed4/3]] || 17.85 || [[6ed9/7]] || 13.63 || [[6ed5/4]] || 10.75 || [[6ed11/9]] || 8.70 || [[6ed6/5]] || 7.18 | |||
|- | |||
| [[7ed3/1]] || 113.17 || [[7ed2/1]] || 16.24 || [[7ed5/3]] || 7.30 || [[7ed3/2]] || 14.80 || [[7ed7/5]] || 17.22 || [[7ed4/3]] || 17.73 || [[7ed9/7]] || 17.45 || [[7ed5/4]] || 16.84 || [[7ed11/9]] || 16.12 || [[7ed6/5]] || 15.36 | |||
|- | |||
| [[8ed3/1]] || 11.28 || [[8ed2/1]] || 48.04 || [[8ed5/3]] || 54.68 || [[8ed3/2]] || 35.34 || [[8ed7/5]] || 24.39 || [[8ed4/3]] || 17.85 || [[8ed9/7]] || 13.63 || [[8ed5/4]] || 10.75 || [[8ed11/9]] || 8.70 || [[8ed6/5]] || 7.18 | |||
|- | |||
| [[9ed3/1]] || 67.97 || [[9ed2/1]] || 35.29 || [[9ed5/3]] || 6.73 || [[9ed3/2]] || 3.66 || [[9ed7/5]] || 7.98 || [[9ed4/3]] || 9.82 || [[9ed9/7]] || 10.54 || [[9ed5/4]] || 10.71 || [[9ed11/9]] || 10.60 || [[9ed6/5]] || 10.35 | |||
|- | |||
| [[10ed3/1]] || 58.83 || [[10ed2/1]] || 18.04 || [[10ed5/3]] || 32.57 || [[10ed3/2]] || 34.86 || [[10ed7/5]] || 24.39 || [[10ed4/3]] || 17.85 || [[10ed9/7]] || 13.63 || [[10ed5/4]] || 10.75 || [[10ed11/9]] || 8.70 || [[10ed6/5]] || 7.18 | |||
|- | |||
| [[11ed3/1]] || 10.34 || [[11ed2/1]] || 47.41 || [[11ed5/3]] || 15.67 || [[11ed3/2]] || 3.43 || [[11ed7/5]] || 2.09 || [[11ed4/3]] || 4.79 || [[11ed9/7]] || 6.14 || [[11ed5/4]] || 6.81 || [[11ed11/9]] || 7.09 || [[11ed6/5]] || 7.16 | |||
|- | |||
| [[12ed3/1]] || 67.97 || [[12ed2/1]] || 1.96 || [[12ed5/3]] || 17.83 || [[12ed3/2]] || 23.16 || [[12ed7/5]] || 24.16 || [[12ed4/3]] || 17.85 || [[12ed9/7]] || 13.63 || [[12ed5/4]] || 10.75 || [[12ed11/9]] || 8.70 || [[12ed6/5]] || 7.18 | |||
|- | |||
| [[13ed3/1]] || 29.57 || [[13ed2/1]] || 36.51 || [[13ed5/3]] || 21.85 || [[13ed3/2]] || 8.34 || [[13ed7/5]] || 1.98 || [[13ed4/3]] || 1.31 || [[13ed9/7]] || 3.10 || [[13ed5/4]] || 4.11 || [[13ed11/9]] || 4.66 || [[13ed6/5]] || 4.96 | |||
|- | |||
| [[14ed3/1]] || 22.69 || [[14ed2/1]] || 16.24 || [[14ed5/3]] || 7.30 || [[14ed3/2]] || 14.80 || [[14ed7/5]] || 17.22 || [[14ed4/3]] || 17.73 || [[14ed9/7]] || 13.63 || [[14ed5/4]] || 10.75 || [[14ed11/9]] || 8.70 || [[14ed6/5]] || 7.18 | |||
|- | |||
| [[15ed3/1]] || 58.83 || [[15ed2/1]] || 18.04 || [[15ed5/3]] || 26.39 || [[15ed3/2]] || 11.94 || [[15ed7/5]] || 4.97 || [[15ed4/3]] || 1.25 || [[15ed9/7]] || 0.87 || [[15ed5/4]] || 2.12 || [[15ed11/9]] || 2.88 || [[15ed6/5]] || 3.34 | |||
|- | |||
| [[16ed3/1]] || 11.28 || [[16ed2/1]] || 26.96 || [[16ed5/3]] || 0.59 || [[16ed3/2]] || 8.54 || [[16ed7/5]] || 12.02 || [[16ed4/3]] || 13.28 || [[16ed9/7]] || 13.56 || [[16ed5/4]] || 10.75 || [[16ed11/9]] || 8.70 || [[16ed6/5]] || 7.18 | |||
|- | |||
| [[17ed3/1]] || 30.68 || [[17ed2/1]] || 3.93 || [[17ed5/3]] || 22.17 || [[17ed3/2]] || 14.69 || [[17ed7/5]] || 7.25 || [[17ed4/3]] || 3.20 || [[17ed9/7]] || 0.84 || [[17ed5/4]] || 0.61 || [[17ed11/9]] || 1.52 || [[17ed6/5]] || 2.10 | |||
|- | |||
| [[18ed3/1]] || 37.69 || [[18ed2/1]] || 31.38 || [[18ed5/3]] || 6.73 || [[18ed3/2]] || 3.66 || [[18ed7/5]] || 7.98 || [[18ed4/3]] || 9.82 || [[18ed9/7]] || 10.54 || [[18ed5/4]] || 10.71 || [[18ed11/9]] || 8.70 || [[18ed6/5]] || 7.18 | |||
|- | |||
| [[19ed3/1]] || 1.23 || [[19ed2/1]] || 7.22 || [[19ed5/3]] || 13.95 || [[19ed3/2]] || 16.86 || [[19ed7/5]] || 9.06 || [[19ed4/3]] || 4.74 || [[19ed9/7]] || 2.18 || [[19ed5/4]] || 0.59 || [[19ed11/9]] || 0.44 || [[19ed6/5]] || 1.12 | |||
|- | |||
| [[20ed3/1]] || 36.27 || [[20ed2/1]] || 18.04 || [[20ed5/3]] || 11.65 || [[20ed3/2]] || 0.24 || [[20ed7/5]] || 4.74 || [[20ed4/3]] || 7.05 || [[20ed9/7]] || 8.12 || [[20ed5/4]] || 8.56 || [[20ed11/9]] || 8.67 || [[20ed6/5]] || 7.18 | |||
|- | |||
| [[21ed3/1]] || 22.60 || [[21ed2/1]] || 16.24 || [[21ed5/3]] || 7.30 || [[21ed3/2]] || 14.80 || [[21ed7/5]] || 10.52 || [[21ed4/3]] || 5.99 || [[21ed9/7]] || 3.27 || [[21ed5/4]] || 1.56 || [[21ed11/9]] || 0.43 || [[21ed6/5]] || 0.33 | |||
|- | |||
| [[22ed3/1]] || 10.34 || [[22ed2/1]] || 7.14 || [[22ed5/3]] || 15.67 || [[22ed3/2]] || 3.43 || [[22ed7/5]] || 2.09 || [[22ed4/3]] || 4.79 || [[22ed9/7]] || 6.14 || [[22ed5/4]] || 6.81 || [[22ed11/9]] || 7.09 || [[22ed6/5]] || 7.16 | |||
|- | |||
| [[23ed3/1]] || 40.41 || [[23ed2/1]] || 23.69 || [[23ed5/3]] || 1.81 || [[23ed3/2]] || 10.44 || [[23ed7/5]] || 11.72 || [[23ed4/3]] || 7.02 || [[23ed9/7]] || 4.17 || [[23ed5/4]] || 2.36 || [[23ed11/9]] || 1.15 || [[23ed6/5]] || 0.32 | |||
|- | |||
| [[24ed3/1]] || 11.28 || [[24ed2/1]] || 1.96 || [[24ed5/3]] || 17.83 || [[24ed3/2]] || 6.09 || [[24ed7/5]] || 0.11 || [[24ed4/3]] || 2.90 || [[24ed9/7]] || 4.50 || [[24ed5/4]] || 5.34 || [[24ed11/9]] || 5.78 || [[24ed6/5]] || 5.97 | |||
|- | |||
| [[25ed3/1]] || 17.25 || [[25ed2/1]] || 18.04 || [[25ed5/3]] || 2.80 || [[25ed3/2]] || 6.78 || [[25ed7/5]] || 10.57 || [[25ed4/3]] || 7.89 || [[25ed9/7]] || 4.93 || [[25ed5/4]] || 3.03 || [[25ed11/9]] || 1.75 || [[25ed6/5]] || 0.87 | |||
|- | |||
| [[26ed3/1]] || 29.57 || [[26ed2/1]] || 9.65 || [[26ed5/3]] || 12.16 || [[26ed3/2]] || 8.34 || [[26ed7/5]] || 1.98 || [[26ed4/3]] || 1.31 || [[26ed9/7]] || 3.10 || [[26ed5/4]] || 4.11 || [[26ed11/9]] || 4.66 || [[26ed6/5]] || 4.96 | |||
|- | |||
| [[27ed3/1]] || 2.47 || [[27ed2/1]] || 9.16 || [[27ed5/3]] || 6.73 || [[27ed3/2]] || 3.66 || [[27ed7/5]] || 7.98 || [[27ed4/3]] || 8.63 || [[27ed9/7]] || 5.57 || [[27ed5/4]] || 3.60 || [[27ed11/9]] || 2.27 || [[27ed6/5]] || 1.34 | |||
|- | |||
| [[28ed3/1]] || 22.69 || [[28ed2/1]] || 16.24 || [[28ed5/3]] || 7.30 || [[28ed3/2]] || 10.27 || [[28ed7/5]] || 3.58 || [[28ed4/3]] || 0.06 || [[28ed9/7]] || 1.91 || [[28ed5/4]] || 3.04 || [[28ed11/9]] || 3.71 || [[28ed6/5]] || 4.09 | |||
|- | |||
| [[29ed3/1]] || 19.48 || [[29ed2/1]] || 1.49 || [[29ed5/3]] || 10.12 || [[29ed3/2]] || 0.97 || [[29ed7/5]] || 5.74 || [[29ed4/3]] || 7.91 || [[29ed9/7]] || 6.13 || [[29ed5/4]] || 4.09 || [[29ed11/9]] || 2.71 || [[29ed6/5]] || 1.74 | |||
|- | |||
| [[30ed3/1]] || 4.57 || [[30ed2/1]] || 18.04 || [[30ed5/3]] || 3.09 || [[30ed3/2]] || 11.46 || [[30ed7/5]] || 4.97 || [[30ed4/3]] || 1.25 || [[30ed9/7]] || 0.87 || [[30ed5/4]] || 2.12 || [[30ed11/9]] || 2.88 || [[30ed6/5]] || 3.34 | |||
|- | |||
| [[31ed3/1]] || 27.07 || [[31ed2/1]] || 5.18 || [[31ed5/3]] || 13.07 || [[31ed3/2]] || 1.37 || [[31ed7/5]] || 3.80 || [[31ed4/3]] || 6.25 || [[31ed9/7]] || 6.61 || [[31ed5/4]] || 4.52 || [[31ed11/9]] || 3.10 || [[31ed6/5]] || 2.09 | |||
|- | |||
| [[32ed3/1]] || 11.28 || [[32ed2/1]] || 10.54 || [[32ed5/3]] || 0.59 || [[32ed3/2]] || 8.54 || [[32ed7/5]] || 6.18 || [[32ed4/3]] || 2.28 || [[32ed9/7]] || 0.04 || [[32ed5/4]] || 1.32 || [[32ed11/9]] || 2.16 || [[32ed6/5]] || 2.68 | |||
|- | |||
| [[33ed3/1]] || 10.34 || [[33ed2/1]] || 11.05 || [[33ed5/3]] || 11.13 || [[33ed3/2]] || 3.43 || [[33ed7/5]] || 2.09 || [[33ed4/3]] || 4.79 || [[33ed9/7]] || 6.14 || [[33ed5/4]] || 4.90 || [[33ed11/9]] || 3.44 || [[33ed6/5]] || 2.40 | |||
|- | |||
| [[34ed3/1]] || 25.26 || [[34ed2/1]] || 3.93 || [[34ed5/3]] || 3.84 || [[34ed3/2]] || 5.96 || [[34ed7/5]] || 7.25 || [[34ed4/3]] || 3.20 || [[34ed9/7]] || 0.84 || [[34ed5/4]] || 0.61 || [[34ed11/9]] || 1.52 || [[34ed6/5]] || 2.10 | |||
|- | |||
| [[35ed3/1]] || 4.49 || [[35ed2/1]] || 16.24 || [[35ed5/3]] || 7.30 || [[35ed3/2]] || 5.25 || [[35ed7/5]] || 0.58 || [[35ed4/3]] || 3.50 || [[35ed9/7]] || 5.01 || [[35ed5/4]] || 5.23 || [[35ed11/9]] || 3.74 || [[35ed6/5]] || 2.67 | |||
|- | |||
| [[36ed3/1]] || 15.14 || [[36ed2/1]] || 1.96 || [[36ed5/3]] || 6.73 || [[36ed3/2]] || 3.66 || [[36ed7/5]] || 7.98 || [[36ed4/3]] || 4.01 || [[36ed9/7]] || 1.55 || [[36ed5/4]] || 0.02 || [[36ed11/9]] || 0.95 || [[36ed6/5]] || 1.58 | |||
|- | |||
| [[37ed3/1]] || 17.70 || [[37ed2/1]] || 11.56 || [[37ed5/3]] || 3.89 || [[37ed3/2]] || 6.88 || [[37ed7/5]] || 0.77 || [[37ed4/3]] || 2.34 || [[37ed9/7]] || 4.01 || [[37ed5/4]] || 4.91 || [[37ed11/9]] || 4.01 || [[37ed6/5]] || 2.92 | |||
|- | |||
| [[38ed3/1]] || 1.23 || [[38ed2/1]] || 7.22 || [[38ed5/3]] || 9.32 || [[38ed3/2]] || 1.61 || [[38ed7/5]] || 6.27 || [[38ed4/3]] || 4.74 || [[38ed9/7]] || 2.18 || [[38ed5/4]] || 0.59 || [[38ed11/9]] || 0.44 || [[38ed6/5]] || 1.12 | |||
|- | |||
| [[39ed3/1]] || 19.20 || [[39ed2/1]] || 5.74 || [[39ed5/3]] || 0.82 || [[39ed3/2]] || 8.34 || [[39ed7/5]] || 1.98 || [[39ed4/3]] || 1.31 || [[39ed9/7]] || 3.10 || [[39ed5/4]] || 4.11 || [[39ed11/9]] || 4.25 || [[39ed6/5]] || 3.14 | |||
|- | |||
| [[40ed3/1]] || 11.28 || [[40ed2/1]] || 11.96 || [[40ed5/3]] || 10.46 || [[40ed3/2]] || 0.24 || [[40ed7/5]] || 4.74 || [[40ed4/3]] || 5.40 || [[40ed9/7]] || 2.75 || [[40ed5/4]] || 1.10 || [[40ed11/9]] || 0.01 || [[40ed6/5]] || 0.71 | |||
|- | |||
| [[41ed3/1]] || 6.12 || [[41ed2/1]] || 0.48 || [[41ed5/3]] || 1.94 || [[41ed3/2]] || 7.47 || [[41ed7/5]] || 3.07 || [[41ed4/3]] || 0.37 || [[41ed9/7]] || 2.29 || [[41ed5/4]] || 3.38 || [[41ed11/9]] || 4.01 || [[41ed6/5]] || 3.33 | |||
|- | |||
| [[42ed3/1]] || 22.60 || [[42ed2/1]] || 12.33 || [[42ed5/3]] || 7.30 || [[42ed3/2]] || 1.91 || [[42ed7/5]] || 3.35 || [[42ed4/3]] || 5.87 || [[42ed9/7]] || 3.27 || [[42ed5/4]] || 1.56 || [[42ed11/9]] || 0.43 || [[42ed6/5]] || 0.33 | |||
|- | |||
| [[43ed3/1]] || 5.75 || [[43ed2/1]] || 4.28 || [[43ed5/3]] || 4.45 || [[43ed3/2]] || 5.48 || [[43ed7/5]] || 4.06 || [[43ed4/3]] || 0.47 || [[43ed9/7]] || 1.55 || [[43ed5/4]] || 2.72 || [[43ed11/9]] || 3.42 || [[43ed6/5]] || 3.51 | |||
|- | |||
| [[44ed3/1]] || 10.34 || [[44ed2/1]] || 7.14 || [[44ed5/3]] || 4.43 || [[44ed3/2]] || 3.43 || [[44ed7/5]] || 2.09 || [[44ed4/3]] || 4.79 || [[44ed9/7]] || 3.74 || [[44ed5/4]] || 1.97 || [[44ed11/9]] || 0.80 || [[44ed6/5]] || 0.01 | |||
|- | |||
| [[45ed3/1]] || 16.56 || [[45ed2/1]] || 8.62 || [[45ed5/3]] || 6.73 || [[45ed3/2]] || 3.66 || [[45ed7/5]] || 4.97 || [[45ed4/3]] || 1.25 || [[45ed9/7]] || 0.87 || [[45ed5/4]] || 2.12 || [[45ed11/9]] || 2.88 || [[45ed6/5]] || 3.34 | |||
|- | |||
| [[46ed3/1]] || 0.94 || [[46ed2/1]] || 2.39 || [[46ed5/3]] || 1.81 || [[46ed3/2]] || 4.82 || [[46ed7/5]] || 0.94 || [[46ed4/3]] || 3.81 || [[46ed9/7]] || 4.17 || [[46ed5/4]] || 2.36 || [[46ed11/9]] || 1.15 || [[46ed6/5]] || 0.32 | |||
|- | |||
| [[47ed3/1]] || 14.01 || [[47ed2/1]] || 12.59 || [[47ed5/3]] || 8.83 || [[47ed3/2]] || 2.00 || [[47ed7/5]] || 5.79 || [[47ed4/3]] || 1.95 || [[47ed9/7]] || 0.25 || [[47ed5/4]] || 1.58 || [[47ed11/9]] || 2.39 || [[47ed6/5]] || 2.89 | |||
|- | |||
| [[48ed3/1]] || 11.28 || [[48ed2/1]] || 1.96 || [[48ed5/3]] || 0.59 || [[48ed3/2]] || 6.09 || [[48ed7/5]] || 0.11 || [[48ed4/3]] || 2.90 || [[48ed9/7]] || 4.50 || [[48ed5/4]] || 2.70 || [[48ed11/9]] || 1.46 || [[48ed6/5]] || 0.61 | |||
|- | |||
| [[49ed3/1]] || 3.28 || [[49ed2/1]] || 8.25 || [[49ed5/3]] || 7.30 || [[49ed3/2]] || 0.48 || [[49ed7/5]] || 5.33 || [[49ed4/3]] || 2.60 || [[49ed9/7]] || 0.31 || [[49ed5/4]] || 1.07 || [[49ed11/9]] || 1.94 || [[49ed6/5]] || 2.48 | |||
|- | |||
| [[50ed3/1]] || 17.25 || [[50ed2/1]] || 5.96 || [[50ed5/3]] || 2.80 || [[50ed3/2]] || 6.78 || [[50ed7/5]] || 1.08 || [[50ed4/3]] || 2.07 || [[50ed9/7]] || 3.77 || [[50ed5/4]] || 3.03 || [[50ed11/9]] || 1.75 || [[50ed6/5]] || 0.87 | |||
|- | |||
| [[51ed3/1]] || 6.62 || [[51ed2/1]] || 3.93 || [[51ed5/3]] || 4.83 || [[51ed3/2]] || 0.93 || [[51ed7/5]] || 4.17 || [[51ed4/3]] || 3.20 || [[51ed9/7]] || 0.84 || [[51ed5/4]] || 0.61 || [[51ed11/9]] || 1.52 || [[51ed6/5]] || 2.10 | |||
|- | |||
| [[52ed3/1]] || 7.01 || [[52ed2/1]] || 9.65 || [[52ed5/3]] || 4.84 || [[52ed3/2]] || 5.16 || [[52ed7/5]] || 1.98 || [[52ed4/3]] || 1.31 || [[52ed9/7]] || 3.10 || [[52ed5/4]] || 3.32 || [[52ed11/9]] || 2.02 || [[52ed6/5]] || 1.11 | |||
|- | |||
| [[53ed3/1]] || 15.76 || [[53ed2/1]] || 0.07 || [[53ed5/3]] || 2.54 || [[53ed3/2]] || 2.23 || [[53ed7/5]] || 3.09 || [[53ed4/3]] || 3.75 || [[53ed9/7]] || 1.32 || [[53ed5/4]] || 0.18 || [[53ed11/9]] || 1.13 || [[53ed6/5]] || 1.75 | |||
|- | |||
| [[54ed3/1]] || 2.47 || [[54ed2/1]] || 9.16 || [[54ed5/3]] || 6.73 || [[54ed3/2]] || 3.66 || [[54ed7/5]] || 2.81 || [[54ed4/3]] || 0.60 || [[54ed9/7]] || 2.48 || [[54ed5/4]] || 3.55 || [[54ed11/9]] || 2.27 || [[54ed6/5]] || 1.34 | |||
|- | |||
| [[55ed3/1]] || 10.34 || [[55ed2/1]] || 3.77 || [[55ed5/3]] || 0.41 || [[55ed3/2]] || 3.43 || [[55ed7/5]] || 2.09 || [[55ed4/3]] || 4.27 || [[55ed9/7]] || 1.77 || [[55ed5/4]] || 0.22 || [[55ed11/9]] || 0.78 || [[55ed6/5]] || 1.42 | |||
|- | |||
| [[56ed3/1]] || 11.28 || [[56ed2/1]] || 5.19 || [[56ed5/3]] || 7.30 || [[56ed3/2]] || 2.27 || [[56ed7/5]] || 3.58 || [[56ed4/3]] || 0.06 || [[56ed9/7]] || 1.91 || [[56ed5/4]] || 3.04 || [[56ed11/9]] || 2.50 || [[56ed6/5]] || 1.55 | |||
|- | |||
| [[57ed3/1]] || 1.23 || [[57ed2/1]] || 7.22 || [[57ed5/3]] || 1.56 || [[57ed3/2]] || 4.55 || [[57ed7/5]] || 1.16 || [[57ed4/3]] || 4.00 || [[57ed9/7]] || 2.18 || [[57ed5/4]] || 0.59 || [[57ed11/9]] || 0.44 || [[57ed6/5]] || 1.12 | |||
|- | |||
| [[58ed3/1]] || 13.32 || [[58ed2/1]] || 1.49 || [[58ed5/3]] || 5.12 || [[58ed3/2]] || 0.97 || [[58ed7/5]] || 4.30 || [[58ed4/3]] || 0.67 || [[58ed9/7]] || 1.37 || [[58ed5/4]] || 2.57 || [[58ed11/9]] || 2.71 || [[58ed6/5]] || 1.74 | |||
|- | |||
| [[59ed3/1]] || 7.25 || [[59ed2/1]] || 9.91 || [[59ed5/3]] || 3.40 || [[59ed3/2]] || 5.59 || [[59ed7/5]] || 0.30 || [[59ed4/3]] || 3.26 || [[59ed9/7]] || 2.57 || [[59ed5/4]] || 0.93 || [[59ed11/9]] || 0.13 || [[59ed6/5]] || 0.84 | |||
|- | |||
| [[60ed3/1]] || 4.57 || [[60ed2/1]] || 1.96 || [[60ed5/3]] || 3.09 || [[60ed3/2]] || 0.24 || [[60ed7/5]] || 4.74 || [[60ed4/3]] || 1.25 || [[60ed9/7]] || 0.87 || [[60ed5/4]] || 2.12 || [[60ed11/9]] || 2.88 || [[60ed6/5]] || 1.92 | |||
|- | |||
| [[61ed3/1]] || 15.18 || [[61ed2/1]] || 6.24 || [[61ed5/3]] || 5.12 || [[61ed3/2]] || 4.94 || [[61ed7/5]] || 0.51 || [[61ed4/3]] || 2.56 || [[61ed9/7]] || 2.93 || [[61ed5/4]] || 1.25 || [[61ed11/9]] || 0.16 || [[61ed6/5]] || 0.58 | |||
|- | |||
| [[62ed3/1]] || 3.61 || [[62ed2/1]] || 5.18 || [[62ed5/3]] || 1.19 || [[62ed3/2]] || 1.37 || [[62ed7/5]] || 3.80 || [[62ed4/3]] || 1.78 || [[62ed9/7]] || 0.40 || [[62ed5/4]] || 1.71 || [[62ed11/9]] || 2.51 || [[62ed6/5]] || 2.09 | |||
|- | |||
| [[63ed3/1]] || 7.59 || [[63ed2/1]] || 2.81 || [[63ed5/3]] || 6.73 || [[63ed3/2]] || 3.66 || [[63ed7/5]] || 1.27 || [[63ed4/3]] || 1.92 || [[63ed9/7]] || 3.27 || [[63ed5/4]] || 1.56 || [[63ed11/9]] || 0.43 || [[63ed6/5]] || 0.33 | |||
|- | |||
| [[64ed3/1]] || 11.28 || [[64ed2/1]] || 8.21 || [[64ed5/3]] || 0.59 || [[64ed3/2]] || 2.43 || [[64ed7/5]] || 2.92 || [[64ed4/3]] || 2.28 || [[64ed9/7]] || 0.04 || [[64ed5/4]] || 1.32 || [[64ed11/9]] || 2.16 || [[64ed6/5]] || 2.25 | |||
|- | |||
| [[65ed3/1]] || 0.31 || [[65ed2/1]] || 0.42 || [[65ed5/3]] || 5.36 || [[65ed3/2]] || 2.46 || [[65ed7/5]] || 1.98 || [[65ed4/3]] || 1.31 || [[65ed9/7]] || 3.10 || [[65ed5/4]] || 1.84 || [[65ed11/9]] || 0.68 || [[65ed6/5]] || 0.10 | |||
|- | |||
| [[66ed3/1]] || 10.34 || [[66ed2/1]] || 7.14 || [[66ed5/3]] || 2.27 || [[66ed3/2]] || 3.43 || [[66ed7/5]] || 2.09 || [[66ed4/3]] || 2.76 || [[66ed9/7]] || 0.45 || [[66ed5/4]] || 0.95 || [[66ed11/9]] || 1.83 || [[66ed6/5]] || 2.38 | |||
|- | |||
| [[67ed3/1]] || 7.73 || [[67ed2/1]] || 3.45 || [[67ed5/3]] || 3.53 || [[67ed3/2]] || 1.33 || [[67ed7/5]] || 2.65 || [[67ed4/3]] || 0.74 || [[67ed9/7]] || 2.60 || [[67ed5/4]] || 2.10 || [[67ed11/9]] || 0.92 || [[67ed6/5]] || 0.12 | |||
|- | |||
| [[68ed3/1]] || 2.71 || [[68ed2/1]] || 3.93 || [[68ed5/3]] || 3.84 || [[68ed3/2]] || 4.37 || [[68ed7/5]] || 1.31 || [[68ed4/3]] || 3.20 || [[68ed9/7]] || 0.84 || [[68ed5/4]] || 0.61 || [[68ed11/9]] || 1.52 || [[68ed6/5]] || 2.10 | |||
|- | |||
| [[69ed3/1]] || 12.84 || [[69ed2/1]] || 6.30 || [[69ed5/3]] || 1.81 || [[69ed3/2]] || 0.27 || [[69ed7/5]] || 3.28 || [[69ed4/3]] || 0.20 || [[69ed9/7]] || 2.13 || [[69ed5/4]] || 2.36 || [[69ed11/9]] || 1.15 || [[69ed6/5]] || 0.32 | |||
|- | |||
| [[70ed3/1]] || 4.49 || [[70ed2/1]] || 0.90 || [[70ed5/3]] || 5.33 || [[70ed3/2]] || 4.78 || [[70ed7/5]] || 0.58 || [[70ed4/3]] || 3.50 || [[70ed9/7]] || 1.20 || [[70ed5/4]] || 0.28 || [[70ed11/9]] || 1.23 || [[70ed6/5]] || 1.83 | |||
|- | |||
| [[71ed3/1]] || 5.46 || [[71ed2/1]] || 7.90 || [[71ed5/3]] || 0.19 || [[71ed3/2]] || 0.73 || [[71ed7/5]] || 3.87 || [[71ed4/3]] || 0.31 || [[71ed9/7]] || 1.69 || [[71ed5/4]] || 2.59 || [[71ed11/9]] || 1.36 || [[71ed6/5]] || 0.52 | |||
|- | |||
| [[72ed3/1]] || 11.28 || [[72ed2/1]] || 1.96 || [[72ed5/3]] || 5.55 || [[72ed3/2]] || 3.66 || [[72ed7/5]] || 0.11 || [[72ed4/3]] || 2.90 || [[72ed9/7]] || 1.55 || [[72ed5/4]] || 0.02 || [[72ed11/9]] || 0.95 || [[72ed6/5]] || 1.58 | |||
|- | |||
| [[73ed3/1]] || 1.51 || [[73ed2/1]] || 4.89 || [[73ed5/3]] || 1.35 || [[73ed3/2]] || 1.68 || [[73ed7/5]] || 3.54 || [[73ed4/3]] || 0.79 || [[73ed9/7]] || 1.27 || [[73ed5/4]] || 2.48 || [[73ed11/9]] || 1.56 || [[73ed6/5]] || 0.70 | |||
|- | |||
| [[74ed3/1]] || 8.00 || [[74ed2/1]] || 4.66 || [[74ed5/3]] || 3.89 || [[74ed3/2]] || 2.61 || [[74ed7/5]] || 0.77 || [[74ed4/3]] || 2.34 || [[74ed9/7]] || 1.87 || [[74ed5/4]] || 0.31 || [[74ed11/9]] || 0.69 || [[74ed6/5]] || 1.35 | |||
|- | |||
| [[75ed3/1]] || 8.11 || [[75ed2/1]] || 2.04 || [[75ed5/3]] || 2.80 || [[75ed3/2]] || 2.58 || [[75ed7/5]] || 2.80 || [[75ed4/3]] || 1.25 || [[75ed9/7]] || 0.87 || [[75ed5/4]] || 2.12 || [[75ed11/9]] || 1.75 || [[75ed6/5]] || 0.87 | |||
|- | |||
| [[76ed3/1]] || 1.23 || [[76ed2/1]] || 7.22 || [[76ed5/3]] || 2.32 || [[76ed3/2]] || 1.61 || [[76ed7/5]] || 1.39 || [[76ed4/3]] || 1.81 || [[76ed9/7]] || 2.18 || [[76ed5/4]] || 0.59 || [[76ed11/9]] || 0.44 || [[76ed6/5]] || 1.12 | |||
|- | |||
| [[77ed3/1]] || 10.34 || [[77ed2/1]] || 0.66 || [[77ed5/3]] || 4.18 || [[77ed3/2]] || 3.43 || [[77ed7/5]] || 2.09 || [[77ed4/3]] || 1.68 || [[77ed9/7]] || 0.49 || [[77ed5/4]] || 1.79 || [[77ed11/9]] || 1.93 || [[77ed6/5]] || 1.03 | |||
|- | |||
| [[78ed3/1]] || 5.18 || [[78ed2/1]] || 5.74 || [[78ed5/3]] || 0.82 || [[78ed3/2]] || 0.66 || [[78ed7/5]] || 1.98 || [[78ed4/3]] || 1.31 || [[78ed9/7]] || 2.48 || [[78ed5/4]] || 0.85 || [[78ed11/9]] || 0.21 || [[78ed6/5]] || 0.91 | |||
|- | |||
| [[79ed3/1]] || 3.77 || [[79ed2/1]] || 3.22 || [[79ed5/3]] || 5.49 || [[79ed3/2]] || 4.24 || [[79ed7/5]] || 1.42 || [[79ed4/3]] || 2.09 || [[79ed9/7]] || 0.14 || [[79ed5/4]] || 1.47 || [[79ed11/9]] || 2.10 || [[79ed6/5]] || 1.19 | |||
|- | |||
| [[80ed3/1]] || 11.28 || [[80ed2/1]] || 3.04 || [[80ed5/3]] || 0.59 || [[80ed3/2]] || 0.24 || [[80ed7/5]] || 2.54 || [[80ed4/3]] || 0.83 || [[80ed9/7]] || 2.68 || [[80ed5/4]] || 1.10 || [[80ed11/9]] || 0.01 || [[80ed6/5]] || 0.71 | |||
|- | |||
| [[81ed3/1]] || 2.47 || [[81ed2/1]] || 5.66 || [[81ed5/3]] || 4.18 || [[81ed3/2]] || 3.66 || [[81ed7/5]] || 0.79 || [[81ed4/3]] || 2.48 || [[81ed9/7]] || 0.20 || [[81ed5/4]] || 1.17 || [[81ed11/9]] || 2.02 || [[81ed6/5]] || 1.34 | |||
|- | |||
| [[82ed3/1]] || 6.12 || [[82ed2/1]] || 0.48 || [[82ed5/3]] || 1.94 || [[82ed3/2]] || 1.09 || [[82ed7/5]] || 3.07 || [[82ed4/3]] || 0.37 || [[82ed9/7]] || 2.29 || [[82ed5/4]] || 1.33 || [[82ed11/9]] || 0.23 || [[82ed6/5]] || 0.51 | |||
|- | |||
| [[83ed3/1]] || 8.41 || [[83ed2/1]] || 6.48 || [[83ed5/3]] || 2.74 || [[83ed3/2]] || 2.72 || [[83ed7/5]] || 0.18 || [[83ed4/3]] || 2.85 || [[83ed9/7]] || 0.53 || [[83ed5/4]] || 0.88 || [[83ed11/9]] || 1.76 || [[83ed6/5]] || 1.48 | |||
|- | |||
| [[84ed3/1]] || 0.04 || [[84ed2/1]] || 1.96 || [[84ed5/3]] || 3.23 || [[84ed3/2]] || 1.91 || [[84ed7/5]] || 3.35 || [[84ed4/3]] || 0.06 || [[84ed9/7]] || 1.91 || [[84ed5/4]] || 1.56 || [[84ed11/9]] || 0.43 || [[84ed6/5]] || 0.33 | |||
|- | |||
| [[85ed3/1]] || 8.30 || [[85ed2/1]] || 3.93 || [[85ed5/3]] || 1.36 || [[85ed3/2]] || 1.83 || [[85ed7/5]] || 0.40 || [[85ed4/3]] || 2.66 || [[85ed9/7]] || 0.84 || [[85ed5/4]] || 0.61 || [[85ed11/9]] || 1.52 || [[85ed6/5]] || 1.61 | |||
|- | |||
| [[86ed3/1]] || 5.75 || [[86ed2/1]] || 4.28 || [[86ed5/3]] || 4.45 || [[86ed3/2]] || 2.69 || [[86ed7/5]] || 2.71 || [[86ed4/3]] || 0.47 || [[86ed9/7]] || 1.55 || [[86ed5/4]] || 1.77 || [[86ed11/9]] || 0.62 || [[86ed6/5]] || 0.16 | |||
|- | |||
| [[87ed3/1]] || 2.39 || [[87ed2/1]] || 1.49 || [[87ed5/3]] || 0.04 || [[87ed3/2]] || 0.97 || [[87ed7/5]] || 0.95 || [[87ed4/3]] || 2.19 || [[87ed9/7]] || 1.13 || [[87ed5/4]] || 0.35 || [[87ed11/9]] || 1.28 || [[87ed6/5]] || 1.74 | |||
|- | |||
| [[88ed3/1]] || 10.34 || [[88ed2/1]] || 6.50 || [[88ed5/3]] || 4.43 || [[88ed3/2]] || 3.43 || [[88ed7/5]] || 2.09 || [[88ed4/3]] || 0.87 || [[88ed9/7]] || 1.20 || [[88ed5/4]] || 1.97 || [[88ed11/9]] || 0.80 || [[88ed6/5]] || 0.01 | |||
|- | |||
| [[89ed3/1]] || 3.26 || [[89ed2/1]] || 0.83 || [[89ed5/3]] || 1.21 || [[89ed3/2]] || 0.16 || [[89ed7/5]] || 1.48 || [[89ed4/3]] || 1.74 || [[89ed9/7]] || 1.41 || [[89ed5/4]] || 0.10 || [[89ed11/9]] || 1.06 || [[89ed6/5]] || 1.68 | |||
|- | |||
| [[90ed3/1]] || 4.57 || [[90ed2/1]] || 4.71 || [[90ed5/3]] || 3.09 || [[90ed3/2]] || 3.66 || [[90ed7/5]] || 1.50 || [[90ed4/3]] || 1.25 || [[90ed9/7]] || 0.87 || [[90ed5/4]] || 2.12 || [[90ed11/9]] || 0.98 || [[90ed6/5]] || 0.17 | |||
|- | |||
| [[91ed3/1]] || 8.67 || [[91ed2/1]] || 3.05 || [[91ed5/3]] || 2.42 || [[91ed3/2]] || 0.62 || [[91ed7/5]] || 1.98 || [[91ed4/3]] || 1.31 || [[91ed9/7]] || 1.68 || [[91ed5/4]] || 0.14 || [[91ed11/9]] || 0.84 || [[91ed6/5]] || 1.49 | |||
|- | |||
| [[92ed3/1]] || 0.94 || [[92ed2/1]] || 2.39 || [[92ed5/3]] || 1.81 || [[92ed3/2]] || 2.81 || [[92ed7/5]] || 0.94 || [[92ed4/3]] || 1.61 || [[92ed9/7]] || 0.56 || [[92ed5/4]] || 1.84 || [[92ed11/9]] || 1.15 || [[92ed6/5]] || 0.32 | |||
|- | |||
| [[93ed3/1]] || 6.62 || [[93ed2/1]] || 5.18 || [[93ed5/3]] || 3.56 || [[93ed3/2]] || 1.37 || [[93ed7/5]] || 2.46 || [[93ed4/3]] || 0.90 || [[93ed9/7]] || 1.94 || [[93ed5/4]] || 0.37 || [[93ed11/9]] || 0.64 || [[93ed6/5]] || 1.30 | |||
|- | |||
| [[94ed3/1]] || 6.22 || [[94ed2/1]] || 0.17 || [[94ed5/3]] || 0.58 || [[94ed3/2]] || 2.00 || [[94ed7/5]] || 0.40 || [[94ed4/3]] || 1.95 || [[94ed9/7]] || 0.25 || [[94ed5/4]] || 1.58 || [[94ed11/9]] || 1.31 || [[94ed6/5]] || 0.47 | |||
|- | |||
| [[95ed3/1]] || 1.23 || [[95ed2/1]] || 5.41 || [[95ed5/3]] || 4.64 || [[95ed3/2]] || 2.09 || [[95ed7/5]] || 2.92 || [[95ed4/3]] || 0.50 || [[95ed9/7]] || 2.18 || [[95ed5/4]] || 0.59 || [[95ed11/9]] || 0.44 || [[95ed6/5]] || 1.12 | |||
|- | |||
| [[96ed3/1]] || 8.53 || [[96ed2/1]] || 1.96 || [[96ed5/3]] || 0.59 || [[96ed3/2]] || 1.22 || [[96ed7/5]] || 0.11 || [[96ed4/3]] || 2.28 || [[96ed9/7]] || 0.04 || [[96ed5/4]] || 1.32 || [[96ed11/9]] || 1.46 || [[96ed6/5]] || 0.61 | |||
|- | |||
| [[97ed3/1]] || 3.93 || [[97ed2/1]] || 3.20 || [[97ed5/3]] || 3.40 || [[97ed3/2]] || 2.77 || [[97ed7/5]] || 2.64 || [[97ed4/3]] || 0.12 || [[97ed9/7]] || 2.07 || [[97ed5/4]] || 0.80 || [[97ed11/9]] || 0.25 || [[97ed6/5]] || 0.95 | |||
|- | |||
| [[98ed3/1]] || 3.28 || [[98ed2/1]] || 4.00 || [[98ed5/3]] || 1.72 || [[98ed3/2]] || 0.48 || [[98ed7/5]] || 0.61 || [[98ed4/3]] || 2.48 || [[98ed9/7]] || 0.31 || [[98ed5/4]] || 1.07 || [[98ed11/9]] || 1.61 || [[98ed6/5]] || 0.74 | |||
|- | |||
| [[99ed3/1]] || 8.88 || [[99ed2/1]] || 1.08 || [[99ed5/3]] || 2.20 || [[99ed3/2]] || 3.43 || [[99ed7/5]] || 2.09 || [[99ed4/3]] || 0.24 || [[99ed9/7]] || 1.75 || [[99ed5/4]] || 1.00 || [[99ed11/9]] || 0.07 || [[99ed6/5]] || 0.79 | |||
|- | |||
| [[100ed3/1]] || 1.77 || [[100ed2/1]] || 5.96 || [[100ed5/3]] || 2.80 || [[100ed3/2]] || 0.24 || [[100ed7/5]] || 1.08 || [[100ed4/3]] || 2.07 || [[100ed9/7]] || 0.58 || [[100ed5/4]] || 0.84 || [[100ed11/9]] || 1.72 || [[100ed6/5]] || 0.87 | |||
|} | |||
Revision as of 16:32, 29 August 2024
For each pair of superparticular ratios [math]\displaystyle{ {s1}/{s2} }[/math] and [math]\displaystyle{ {s2}/{s3} }[/math], there exists a ratio [math]\displaystyle{ {a}/{b} }[/math] such that [math]\displaystyle{ {s1}/{s2} }[/math] and [math]\displaystyle{ {s2}/{s3} }[/math] are [math]\displaystyle{ {a}/{b} }[/math] complementary; it is observed that [math]\displaystyle{ a−b=1 }[/math] or [math]\displaystyle{ a−b=2 }[/math]. In other words, for each ratio [math]\displaystyle{ a/b }[/math] where [math]\displaystyle{ a−b=1 }[/math] or [math]\displaystyle{ a−b=2 }[/math], there exists a pair of superparticular ratios [math]\displaystyle{ {s1}/{s2} }[/math] and [math]\displaystyle{ {s2}/{s3} }[/math] that are [math]\displaystyle{ {a}/{b} }[/math] complementary.
Bellow is a table that show for equal divisions of [math]\displaystyle{ a/b }[/math] the cent error in the mapping of superparticular ratios [math]\displaystyle{ {s1}/{s2} }[/math] and [math]\displaystyle{ {s2}/{s3} }[/math] that are [math]\displaystyle{ a/b }[/math] complementary.
We can observe a converging sequence and pattern for low errors: 5, 7, 12; then 7, 9, 16; then 9, 11, 20; then 11, 13, 24; then 13, 15, 28; then 15, 17, 32; then 17, 19, 36; then 19, 21, 40; then 21, 23, 44; etc. --
| Todo: Table
Show the table for 3/1, 2/1, 5/3, 3/2, 7/5, 4/3, 9/7, 5/4, 11/9, 6/5. Highlight the pattern in bold. |