88 is carréphobic - approach of √88=2√22 ~ 9.3808315196
Subsequent approximations of √88 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-88p2 = 1 | | | |
| d = distance to nearest square N2: | +7 | | | |
| Smallest non-trivial s: | (2*81+7)/7 | rational: 169/7 | actual: 197 | ⇒ F=394 |
| Smallest non-trivial p: | 2*9/7 | rational: 18/7 | actual: 21 | ⇒ primus foldage=21 |
| v-value qt-blocks: | 282-88*32: | -8 | | |
| Number of series: | 16 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 197 | 77617 | 30580901 | ... |
| p | 0 | 21 | 8274 | 3259935 | ... |
| In the numerator: | U(1,197)394 | = | 1/2*U(2,394)394 | - | half the secundus of 394. |
| In the denominator: | U(0,21)394 | = | 21*U(0,1)394 | - | the 21-fold primus of 394. |
| as well as ... |
| In the numerator: | U(0,1848)394 | = | 1848*U(0,1)394 | - | the 88*21-fold primus of 394. |
| In the denominator: | U(1,197)394 | = | 1/2*U(2,394)394 | - | half the secundus of 394. |
| and ... |
| In the numerator: | U(-28,28)394 | = | 28*U(-1,1)394 | - | the 28-fold quartus of 394. |
| In the denominator: | U(3,3)394 | = | 3*U(1,1)394 | - | the 3-fold tertius of 394. |
