Blue Sapphire Ratio

[TANAKA]

....7，11，18，29，47，76，123，199，322，521, 843, 1364, 2207, 3571, 5778,
9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851.......

....8×2，5×3，3×5，2×8.......
→....16，15，15，16.......
√16×√15÷7≒2.213133340689

....13×2，8×3，5×5，3×8.......
→....26，24，25，24.......
√26×√25÷11≒2.317736142542

....21×2，13×3，8×5，5×8.......
→....42，39，40，40.......
√42×√40÷18≒2.277100170213

√68×√65÷29≒2.292520019116
√110×√105÷47≒2.286615453213
√178×√170÷76≒2.288868643585
√288×√275÷123≒2.288007687718
√466×√445÷199≒2.288336497802
√754×√720÷322≒2.288210896846
√1220×√1165÷521≒2.288258871167
√1974×√1885÷843≒2.288240546465
√3194×√3050÷1364≒2.288247545857
√5168×√4935÷2207≒2.288244872324
√8362×√7985÷3571≒2.288245893523
√13530×√12920÷5778≒2.288245503459
√21892×√20905÷9349≒2.288245652450
√35422×√33825÷15127≒2.288245595541
√57314×√54730÷24476≒2.288245617278
√92736×√88555÷39603≒2.288245608975
√150050×√143285÷64079≒2.288245612147
√242786×√231840÷103682≒2.288245610935
√392836×√375125÷167761≒2.288245611398
√635622×√606965÷271443≒2.288245611221
√1028458×√982090÷439204≒2.288245611289
√1664080×√1589055÷710647≒2.288245611263
√2692538×√2571145÷1149851≒2.288245611273


Lucas≒Fibonacci≒Pythagoras

1,1,2,3,5,8,13,21,34,55,89,144,233,...
1²,1²,1²+1²,2²-1²,1²+2²,3²-1²,2²+3²,5²-2²,3²+5²,8²-3²,5²+8²,13²-5
²,8²+13²,...

1,1,1+1,2-1,1+2,3-1,2+3,5-2,3+5,8-3,5+8,13-5,8+13,...
1,1,2,1,3,2,5,3,8,5,13,8,21,...

1²,1²,1²+1²,1²,2²-1²,1²+1²,1²+2²,2²-1,3²-1²,1²+2²,2²+3²,3²-1²,5²-
2²,...
1,1,2,1,1,2,3,1,2,3,5,2,3,...

1²,1²,1²+1²,1²,1²,1²+1²,2²-1²,1²,1²+1²,2²-1²,1²+2²,1²+1²,2²-1²,..
.
1,1,2,1,1,2,1,1,2,1,3,2,1,...

1,1,2,1,3,2,5,3,8,5,13,8,21,13,34,21,55,34,89,55,144,89,233,144,3
77,233,610,377,987,610,1597,987,2584,1597,4181,2584,6765,4181,109
46,6765,17711,10946,28657,17711,46368,28657,75025,46368,121393,75
025,196418,121393,317811,196418,514229,317811,832040,514229,13462
69,832040,2178309,1346269,3524578,2178309,5702887,3524578,9227465
,...＠Ｙ．Ｔ．

1,1,2,1,1,2,3,1,2,3,5,2,3,5,8,3,5,8,13,5,8,13,21,8,13,21,34,13,21
,34,55,21,34,55,89,34,55,89,144,55,89,144,233,89,144,233,377,144,
233,377,610,233,377,610,987,377,610,987,1597,610,987,1597,2584,98
7,1597,2584,4181,...

1,1,2,1,1,2,1,1,2,1,3,2,1,3,2,1,3,2,5,3,2,5,3,2,5,3,8,5,3,8,5,3,8
,5,13,8,5,13,8,5,13,8,21,13,8,21,13,8,21,13,34,21,13,34,21,13,34,
21,55,34,21,55,34,21,55,34,89,...

1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2
,3,5,2,3,5,2,3,5,2,3,5,2,3,5,2,3,5,8,3,5,8,3,5,8,3,5,8,3,5,8,3,5,
8,13,...

1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2
,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,2,1,3,
2,5,...


1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,...
2,1,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,...

1,1,2,5,13,34,89,233,610,1597,4181,10946,28657,75025,196418,51422
9,1346269,...
5,5,10,25,65,170,445,1165,3050,7985,20905,54730,143285,375125,982
090,2571145,...

1,3,8,21,55,144,377,987,2584,6765,17711,46368,121393,317811,83204
0,2178309,5702887,...
5,15,40,105,275,720,1885,4935,12920,33825,88555,231840,606965,158
9055,4160200,10891545,...


http://www.altmc.jp/cgi-bin/freegroup/a ... ct=SF;f=19

http://suseum.jp/gd/index/3826

√2(1+√5)/2≒2.288245611270737190400

[TANAKA]

These combinations are solid figures of fractal figures.

Α－Α　Α－Γ　Γ－Γ
Β´－Β´　Β－Δ　Β´－Δ´　Δ´－Δ´　(Β－Ε)

√2:1+√5＝BLUE SAPPHIRE RATIO
LUCAS≒FIBONACCI≒PYTHAGORAS is another topic.
ENGLISH is difficult, I did my BEST.

GOOD LUCK!