108 is carréphobic - approach of √108=6√3 ~ 10.3923048454
Subsequent approximations of √108 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-108p2 = 1 | | | |
| d = distance to nearest square N2: | +8 | | | |
| Smallest non-trivial s: | (2*100+8)/8 | rational: 26 | actual: 1351 | ⇒ F=2702 |
| Smallest non-trivial p: | 2*10/8 | rational: 20/8 | actual: 130 | ⇒ primus foldage=130 |
| v-value tq-blocks: | 522-108*52: | +4 | | |
| v-value qt-blocks: | 1352-108*132: | -27 | | |
| Number of series: | 21 | | | |
Note that the 'rational s' is an integer, but the 'rational p' is not.
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 1351 | 3650401 | ... |
| p | 0 | 130 | 351260 | ... |
| In the numerator: | U(1,1351)2702 | = | 1/2*U(2,2702)2702 | - | half the secundus of 2702. |
| In the denominator: | U(0,130)2702 | = | 130*U(0,1)2702 | - | the 130-fold primus of 2702. |
| as well as ... |
| In the numerator: | U(0,14040)2702 | = | 14040*U(0,1)2702 | - | the 108*130-fold primus of 2702. |
| In the denominator: | U(1,1351)2702 | = | 1/2*U(2,2702)2702 | - | half the secundus of 2702. |
| and ... |
| In the numerator: | U(52,52)2702 | = | 52*U(1,1)2702 | - | the 52-fold tertius of 2702. |
| In the denominator: | U(-5,5)2702 | = | 5*U(-1,1)2702 | - | the 5-fold quartus of 2702. |
| and ... |
| In the numerator: | U(-135,135)2702 | = | 135*U(-1,1)2702 | - | the 135-fold quartus of 2702. |
| In the denominator: | U(13,13)2702 | = | 13*U(1,1)2702 | - | the 13-fold tertius of 2702. |
