2 is carréphylic - approach of √2 ~ 1.4142135624
Subsequent approximations of √2 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-2p2 = 1 | | | |
| d = distance to nearest square N2: | +1 | | | |
| Smallest non-trivial s: | (2*1+1)/1 | rational: 3 | actual: 3 | ⇒ F=6 |
| Smallest non-trivial p: | 2*1/1 | rational: 2 | actual: 2 | ⇒ primus foldage=2 |
| v-value qt-blocks: | 12-2*12: | -1 | | |
| Number of series: | 3 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 3 | 17 | 99 | 577 | 3363 | 19601 | 114243 | 665857 | 3880899 | ... |
| p | 0 | 2 | 12 | 70 | 408 | 2378 | 13860 | 80782 | 470832 | 2744210 | ... |
| In the numerator: | U(1,3)6 | = | 1/2*U(2,6)6 | - | half the secundus of 6. |
| In the denominator: | U(0,2)6 | = | 2*U(0,1)6 | - | the 2-fold primus of 6. |
| as well as ... |
| In the numerator: | U(0,4)6 | = | 4*U(0,1)6 | - | the 2*2-fold primus of 6. |
| In the denominator: | U(1,3)6 | = | 1/2*U(2,6)6 | - | half the secundus of 6. |
| and ... |
| In the numerator: | U(-1,1)6 | = | | - | the quartus of 6. |
| In the denominator: | U(1,1)6 | = | | - | the tertius of 6. |
