38 is carréphylic - approach of √38 ~ 6.1644140030
Subsequent approximations of √38 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-38p2 = 1 | | | |
| d = distance to nearest square N2: | +2 | | | |
| Smallest non-trivial s: | (2*36+2)/2 | rational: 37 | actual: 37 | ⇒ F=74 |
| Smallest non-trivial p: | 2*6/2 | rational: 6 | actual: 6 | ⇒ primus foldage=6 |
| v-value qt-blocks: | 62-38*12: | -2 | | |
| Number of series: | 10 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 37 | 2737 | 202501 | 14982337 | 1108490437 | ... |
| p | 0 | 6 | 444 | 32850 | 2430456 | 179820894 | ... |
| In the numerator: | U(1,37)74 | = | 1/2*U(2,74)74 | - | half the secundus of 74. |
| In the denominator: | U(0,6)74 | = | 6*U(0,1)74 | - | the 6-fold primus of 74. |
| as well as ... |
| In the numerator: | U(0,228)74 | = | 228*U(0,1)74 | - | the 38*6-fold primus of 74. |
| In the denominator: | U(1,37)74 | = | 1/2*U(2,74)74 | - | half the secundus of 74. |
| and ... |
| In the numerator: | U(-6,6)74 | = | 6*U(-1,1)74 | - | the 6-fold quartus of 74. |
| In the denominator: | U(1,1)74 | = | | - | the tertius of 74. |
