90 is carréphylic - approach of √90=3√10 ~ 9.4868329805
Subsequent approximations of √90 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-90p2 = 1 | | | |
| d = distance to nearest square N2: | +9 | | | |
| Smallest non-trivial s: | (2*81+9)/9 | rational: 19 | actual: 19 | ⇒ F=38 |
| Smallest non-trivial p: | 2*9/9 | rational: 2 | actual: 2 | ⇒ primus foldage=2 |
| v-value qt-blocks: | 92-90*12: | -9 | | |
| Number of series: | 11 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| In the numerator: | U(1,19)38 | = | 1/2*U(2,38)38 | - | half the secundus of 38. |
| In the denominator: | U(0,2)38 | = | 2*U(0,1)38 | - | the 2-fold primus of 38. |
| as well as ... |
| In the numerator: | U(0,180)38 | = | 180*U(0,1)38 | - | the 90*2-fold primus of 38. |
| In the denominator: | U(1,19)38 | = | 1/2*U(2,38)38 | - | half the secundus of 38. |
| and ... |
| In the numerator: | U(-9,9)38 | = | 9*U(-1,1)38 | - | the 9-fold quartus of 38. |
| In the denominator: | U(1,1)38 | = | | - | the tertius of 38. |
