4 is carréphylic - approach of √34 ~ 5.8309518948
Subsequent approximations of √34 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-34p2 = 1 | | | |
| d = distance to nearest square N2: | -2 | | | |
| Smallest non-trivial s: | (2*36-2)/2 | rational: 35 | actual: 35 | ⇒ F=70 |
| Smallest non-trivial p: | 2*6/2 | rational: 6 | actual: 6 | ⇒ primus foldage=6 |
| v-value tq-blocks: | 62-34*12: | +2 | | |
| v-value qt-blocks: | 172-34*32: | -17 | | |
| Number of series: | 11 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 35 | 2449 | 171395 | 11995201 | ... |
| p | 0 | 6 | 420 | 29394 | 2057160 | ... |
| In the numerator: | U(1,35)70 | = | 1/2*U(2,70)70 | - | half the secundus of 70. |
| In the denominator: | U(0,6)70 | = | 6*U(0,1)70 | - | the 6-fold primus of 70. |
| as well as ... |
| In the numerator: | U(0,204)70 | = | 204*U(0,1)70 | - | the 34*6-fold primus of 70. |
| In the denominator: | U(1,35)70 | = | 1/2*U(2,70)70 | - | half the secundus of 70. |
| and ... |
| In the numerator: | U(6,6)70 | = | 6*U(1,1)70 | - | the 6-fold tertius of 70. |
| In the denominator: | U(-1,1)70 | = | | - | the quartus of 70. |
| and ... |
| In the numerator: | U(-17,17)70 | = | 17*U(-1,1)70 | - | the 17-fold quartus of 70. |
| In the denominator: | U(3,3)70 | = | 3*U(1,1)70 | - | the 3-fold tertius of 70. |
