7 is carréphylic - approach of √7 ~ 2.6457513111
Subsequent approximations of √7 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-7p2 = 1 | | | |
| d = distance to nearest square N2: | -2 | | | |
| Smallest non-trivial s: | (2*9-2)/2 | rational: 8 | actual: 8 | ⇒ F=16 |
| Smallest non-trivial p: | 2*3/2 | rational: 3 | actual: 3 | ⇒ primus foldage=3 |
| v-value tq-blocks: | 32-7*12: | +2 | | |
| Number of series: | 6 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 8 | 127 | 2024 | 32257 | 514088 | 8193151 | 130576328 | ... |
| p | 0 | 3 | 48 | 765 | 12192 | 194307 | 3096720 | 49353213 | ... |
| In the numerator: | U(1,8)16 | = | 1/2*U(2,16)16 | - | half the secundus of 16. |
| In the denominator: | U(0,3)16 | = | 3*U(0,1)16 | - | the 3-fold primus of 16. |
| as well as ... |
| In the numerator: | U(0,21)16 | = | 21*U(0,1)16 | - | the 7*3-fold primus of 16. |
| In the denominator: | U(1,8)16 | = | 1/2*U(2,16)16 | - | half the secundus of 16. |
| and ... |
| In the numerator: | U(3,3)16 | = | 3*U(1,1)16 | - | the 3-fold tertius of 16. |
| In the denominator: | U(-1,1)16 | = | | - | the quartus of 16. |
