66 is carréphylic - approach of √66 ~ 8.1240384046
Subsequent approximations of √66 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-66p2 = 1 | | | |
| d = distance to nearest square N2: | +2 | | | |
| Smallest non-trivial s: | (2*64+2)/2 | rational: 65 | actual: 65 | ⇒ F=130 |
| Smallest non-trivial p: | 2*8/2 | rational: 8 | actual: 8 | ⇒ primus foldage=8 |
| v-value qt-blocks: | 82-66*12: | -2 | | |
| Number of series: | 13 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| In the numerator: | U(1,65)130 | = | 1/2*U(2,130)130 | - | half the secundus of 130. |
| In the denominator: | U(0,8)130 | = | 8*U(0,1)130 | - | the 8-fold primus of 130. |
| as well as ... |
| In the numerator: | U(0,528)130 | = | 528*U(0,1)130 | - | the 66*8-fold primus of 130. |
| In the denominator: | U(1,65)130 | = | 1/2*U(2,130)130 | - | half the secundus of 130. |
| and ... |
| In the numerator: | U(-8,8)130 | = | 8*U(-1,1)130 | - | the 8-fold quartus of 130. |
| In the denominator: | U(1,1)130 | = | | - | the tertius of 130. |
