27 is carréphylic - approach of √27=3√3 ~ 5.1961524227
Subsequent approximations of √27 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-27p2 = 1 | | | |
| d = distance to nearest square N2: | +2 | | | |
| Smallest non-trivial s: | (2*25+2)/2 | rational: 26 | actual: 26 | ⇒ F=52 |
| Smallest non-trivial p: | 2*5/2 | rational: 5 | actual: 5 | ⇒ primus foldage=5 |
| v-value qt-blocks: | 52-27*12: | -2 | | |
| Number of series: | 9 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 26 | 1351 | 70226 | 3650401 | 189750626 | ... |
| p | 0 | 5 | 260 | 13515 | 702520 | 36517525 | ... |
| In the numerator: | U(1,26)52 | = | 1/2*U(2,52)52 | - | half the secundus of 52. |
| In the denominator: | U(0,5)52 | = | 5*U(0,1)52 | - | the 5-fold primus of 52. |
| as well as ... |
| In the numerator: | U(0,135)52 | = | 135*U(0,1)52 | - | the 27*5-fold primus of 52. |
| In the denominator: | U(1,26)52 | = | 1/2*U(2,52)52 | - | half the secundus of 52. |
| and ... |
| In the numerator: | U(-5,5)52 | = | 5*U(-1,1)52 | - | the 5-fold quartus of 52. |
| In the denominator: | U(1,1)52 | = | | - | the tertius of 52. |
