6 is carréphylic - approach of √6 ~ 2.4494897428
Subsequent approximations of √6 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-6p2 = 1 | | | |
| d = distance to nearest square N2: | +2 | | | |
| Smallest non-trivial s: | (2*4+2)/2 | rational: 5 | actual: 5 | ⇒ F=10 |
| Smallest non-trivial p: | 2*2/2 | rational: 2 | actual: 2 | ⇒ primus foldage=2 |
| v-value qt-blocks: | 22-6*12: | -2 | | |
| Number of series: | 4 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 5 | 49 | 485 | 4801 | 47525 | 470449 | 4656965 | ... |
| p | 0 | 2 | 20 | 198 | 1960 | 19402 | 192060 | 1901198 | ... |
| In the numerator: | U(1,5)10 | = | 1/2*U(2,10)10 | - | half the secundus of 10. |
| In the denominator: | U(0,2)10 | = | 2*U(0,1)10 | - | the 2-fold primus of 10. |
| as well as ... |
| In the numerator: | U(0,12)10 | = | 12*U(0,1)10 | - | the 6*2-fold primus of 10. |
| In the denominator: | U(1,5)10 | = | 1/2*U(2,10)10 | - | half the secundus of 10. |
| and ... |
| In the numerator: | U(-2,2)10 | = | 2*U(-1,1)10 | - | the 2-fold quartus of 10. |
| In the denominator: | U(1,1)10 | = | | - | the tertius of 10. |
