12 is carréphylic - approach of √12=2√3 ~ 3.4641016151
Subsequent approximations of √12 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-12p2 = 1 | | | |
| d = distance to nearest square N2: | +3 | | | |
| Smallest non-trivial s: | (2*9+3)/3 | rational: 7 | actual: 7 | ⇒ F=14 |
| Smallest non-trivial p: | 2*3/3 | rational: 2 | actual: 2 | ⇒ primus foldage=2 |
| v-value qt-blocks: | 32-12*12: | -3 | | |
| Number of series: | 5 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 7 | 97 | 1351 | 18817 | 262087 | 3650401 | 50843527 | ... |
| p | 0 | 2 | 28 | 390 | 5432 | 75658 | 1053780 | 14677262 | ... |
| In the numerator: | U(1,7)14 | = | 1/2*U(2,14)14 | - | half the secundus of 14. |
| In the denominator: | U(0,2)14 | = | 2*U(0,1)14 | - | the 2-fold primus of 14. |
| as well as ... |
| In the numerator: | U(0,24)14 | = | 24*U(0,1)14 | - | the 12*2-fold primus of 14. |
| In the denominator: | U(1,7)14 | = | 1/2*U(2,14)14 | - | half the secundus of 14. |
| and ... |
| In the numerator: | U(-3,3)14 | = | 3*U(-1,1)14 | - | the 3-fold quartus of 14. |
| In the denominator: | U(1,1)14 | = | | - | the tertius of 14. |
