55 is carréphobic - approach of √55 ~ 7.4161984871
Subsequent approximations of √55 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-55p2 = 1 | | | |
| d = distance to nearest square N2: | +6 | | | |
| Smallest non-trivial s: | (2*49+6)/6 | rational: 104/6 | actual: 89 | ⇒ F=178 |
| Smallest non-trivial p: | 2*7/6 | rational: 14/6 | actual: 12 | ⇒ primus foldage=12 |
| v-value tq-blocks: | 152-55*22: | +5 | | |
| v-value qt-blocks: | 222-55*32: | -11 | | |
| Number of series: | 13 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 89 | 15841 | 2819609 | 501874561 | ...
| p | 0 | 12 | 2136 | 380196 | 67672752 | ... |
| In the numerator: | U(1,89)178 | = | 1/2*U(2,178)178 | - | half the secundus of 178. |
| In the denominator: | U(0,12)178 | = | 12*U(0,1)178 | - | the 12-fold primus of 178. |
| as well as ... |
| In the numerator: | U(0,660)178 | = | 660*U(0,1)178 | - | the 55*12-fold primus of 178. |
| In the denominator: | U(1,89)178 | = | 1/2*U(2,178)178 | - | half the secundus of 178. |
| and ... |
| In the numerator: | U(15,15)178 | = | 15*U(1,1)178 | - | the 15-fold tertius of 178. |
| In the denominator: | U(-2,2)178 | = | 2*U(-1,1)178 | - | the 2-fold quartus of 178. |
| and ... |
| In the numerator: | U(-22,22)178 | = | 22*U(-1,1)178 | - | the 22-fold quartus of 178. |
| In the denominator: | U(3,3)178 | = | 3*U(1,1)178 | - | the 3-fold tertius of 178. |
