37 is carréphylic - approach of √37 ~ 6.0827625303
Subsequent approximations of √37 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-37p2 = 1 | | | |
| d = distance to nearest square N2: | +1 | | | |
| Smallest non-trivial s: | (2*36+1)/1 | rational: 73 | actual: 73 | ⇒ F=146 |
| Smallest non-trivial p: | 2*6/1 | rational: 12 | actual: 12 | ⇒ primus foldage=12 |
| v-value qt-blocks: | 62-37*12: | -1 | | |
| Number of series: | 13 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 73 | 10657 | 1555849 | 227143297 | ... |
| p | 0 | 12 | 1752 | 255780 | 37342128 | ... |
| In the numerator: | U(1,73)146 | = | 1/2*U(2,146)146 | - | half the secundus of 146. |
| In the denominator: | U(0,12)146 | = | 12*U(0,1)146 | - | the 12-fold primus of 146. |
| as well as ... |
| In the numerator: | U(0,444)146 | = | 444*U(0,1)146 | - | the 37*12-fold primus of 146. |
| In the denominator: | U(1,73)146 | = | 1/2*U(2,146)146 | - | half the secundus of 146. |
| and ... |
| In the numerator: | U(-6,6)146 | = | 6*U(-1,1)146 | - | the 6-fold quartus of 146. |
| In the denominator: | U(1,1)146 | = | | - | the tertius of 146. |
