Geometric series | Irrational | Rational | Ratio | r2 | cs | QSF | ||||||
a | b | value | approx. | r | estimates | supercluster | ||||||
a+b*1.5 | rat/irr | 1 − 2*(1 − r) | (order) | |||||||||
0 | = | 0 | = | 0 | 0 | 0 | 0 | 0 | ||||
1 | = | 1 | = | 1 | 1 | 1 | 1 | 1 | ||||
t | = | t | = | 1.61803 | 1.5 | 0.927 | 0.859 | 0.854 | ||||
1 | + | t | = | t2 | = | 2.61803 | 2.5 | 0.955 | 0.912 | 0.91 | ||
1 | + | 2 | t | = | t3 | = | 4.23607 | 4 | 0.944 | 0.891 | 0.888 | |
2 | + | 3 | t | = | t4 | = | 6.8541 | 6.5 | 0.948 | 0.899 | 0.896 | |
3 | + | 5 | t | = | t5 | = | 11.0902 | 10.5 | 0.947 | 0.897 | 0.894 | |
5 | + | 8 | t | = | t6 | = | 17.9443 | 17 | 0.947 | 0.897 | 0.894 | |
8 | + | 13 | t | = | t7 | = | 29.0344 | 27.5 | 0.947 | 0.897 | 0.894 | |
13 | + | 21 | t | = | t8 | = | 46.9787 | 44.5 | 0.947 | 0.897 | 0.894 | sc(2) |
21 | + | 34 | t | = | t9 | = | 76.0132 | 72 | 0.947 | 0.897 | 0.894 | |
34 | + | 55 | t | = | t10 | = | 122.992 | 116.5 | 0.947 | 0.897 | 0.894 | sc(3) |
55 | + | 89 | t | = | t11 | = | 199.005 | 188.5 | 0.947 | 0.897 | 0.894 | |
89 | + | 144 | t | = | t12 | = | 321.997 | 305 | 0.947 | 0.897 | 0.894 | |
144 | + | 233 | t | = | t13 | = | 521.002 | 493.5 | 0.947 | 0.897 | 0.894 | |
233 | + | 377 | t | = | t14 | = | 842.999 | 798.5 | 0.947 | 0.897 | 0.894 | |
377 | + | 610 | t | = | t15 | = | 1364 | 1292 | 0.947 | 0.897 | 0.894 | |
610 | + | 987 | t | = | t16 | = | 2207 | 2090.5 | 0.947 | 0.897 | 0.894 | sc(6) |