11 is carréphylic - approach of √11 ~ 3.3166247904
Subsequent approximations of √11 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-11p2 = 1 | | | |
| d = distance to nearest square N2: | +2 | | | |
| Smallest non-trivial s: | (2*9+2)/2 | rational: 10 | actual: 10 | ⇒ F=20 |
| Smallest non-trivial p: | 2*3/2 | rational: 3 | actual: 3 | ⇒ primus foldage=3 |
| v-value qt-blocks: | 32-11*12: | -2 | | |
| Number of series: | 6 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 10 | 199 | 3970 | 79201 | 1580050 | 31521799 | ... |
| p | 0 | 3 | 60 | 1197 | 23880 | 476403 | 9504180 | ... |
| In the numerator: | U(1,10)20 | = | 1/2*U(2,20)20 | - | half the secundus of 20. |
| In the denominator: | U(0,3)20 | = | 3*U(0,1)20 | - | the 3-fold primus of 20. |
| as well as ... |
| In the numerator: | U(0,33)20 | = | 33*U(0,1)20 | - | the 11*3-fold primus of 20. |
| In the denominator: | U(1,10)20 | = | 1/2*U(2,20)20 | - | half the secundus of 20. |
| and ... |
| In the numerator: | U(-3,3)20 | = | 3*U(-1,1)20 | - | the 3-fold quartus of 20. |
| In the denominator: | U(1,1)20 | = | | - | the tertius of 20. |
