18 is carréphylic - approach of √18=3√2 ~ 4.2426406871
Subsequent approximations of √18 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-18p2 = 1 | | | |
| d = distance to nearest square N2: | +2 | | | |
| Smallest non-trivial s: | (2*16+2)/2 | rational: 17 | actual: 17 | ⇒ F=34 |
| Smallest non-trivial p: | 2*4/2 | rational: 4 | actual: 4 | ⇒ primus foldage=4 |
| v-value qt-blocks: | 42-18*12: | -2 | | |
| Number of series: | 7 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 17 | 577 | 19601 | 665857 | 22619537 | ... |
| p | 0 | 4 | 136 | 4620 | 156944 | 5331476 | ... |
| In the numerator: | U(1,17)34 | = | 1/2*U(2,34)34 | - | half the secundus of 34. |
| In the denominator: | U(0,4)34 | = | 4*U(0,1)34 | - | the 4-fold primus of 34. |
| as well as ... |
| In the numerator: | U(0,72)34 | = | 72*U(0,1)34 | - | the 18*4-fold primus of 34. |
| In the denominator: | U(1,17)34 | = | 1/2*U(2,34)34 | - | half the secundus of 34. |
| and ... |
| In the numerator: | U(-4,4)34 | = | 4*U(-1,1)34 | - | the 4-fold quartus of 34. |
| In the denominator: | U(1,1)34 | = | | - | the tertius of 34. |
