32 is carréphylic - approach of √32=4√2 ~ 5.6568542495
Subsequent approximations of √32 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-32p2 = 1 | | | |
| d = distance to nearest square N2: | -4 | | | |
| Smallest non-trivial s: | (2*36-4)/4 | rational: 17 | actual: 17 | ⇒ F=34 |
| Smallest non-trivial p: | 2*6/4 | rational: 3 | actual: 3 | ⇒ primus foldage=3 |
| v-value tq-blocks: | 62-32*12: | +4 | | |
| Number of series: | 9 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 17 | 577 | 19601 | 665857 | 22619537 | ... |
| p | 0 | 3 | 102 | 3465 | 117708 | 3998607 | ... |
| In the numerator: | U(1,17)34 | = | 1/2*U(2,34)34 | - | half the secundus of 34. |
| In the denominator: | U(0,3)34 | = | 3*U(0,1)34 | - | the 3-fold primus of 34. |
| as well as ... |
| In the numerator: | U(0,96)34 | = | 96*U(0,1)34 | - | the 32*3-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(6,6)34 | = | 6*U(1,1)34 | - | the 6-fold tertius of 34. |
| In the denominator: | U(-1,1)34 | = | | - | the quartus of 34. |
