75 is carréphylic - approach of √75=5√3 ~ 8.6602540378
Subsequent approximations of √75 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-75p2 = 1 | | | |
| d = distance to nearest square N2: | -6 | | | |
| Smallest non-trivial s: | (2*81-6)/6 | rational: 26 | actual: 26 | ⇒ F=52 |
| Smallest non-trivial p: | 2*9/6 | rational: 3 | actual: 3 | ⇒ primus foldage=3 |
| v-value tq-blocks: | 92-75*12: | +6 | | |
| Number of series: | 12 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 26 | 1351 | 70226 | ... |
| p | 0 | 3 | 156 | 8109 | ... |
| In the numerator: | U(1,26)52 | = | 1/2*U(2,52)52 | - | half the secundus of 52. |
| In the denominator: | U(0,3)52 | = | 3*U(0,1)52 | - | the 3-fold primus of 52. |
| as well as ... |
| In the numerator: | U(0,225)52 | = | 225*U(0,1)52 | - | the 75*3-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(9,9)52 | = | 9*U(1,1)52 | - | the 9-fold tertius of 52. |
| In the denominator: | U(-1,1)52 | = | | - | the quartus of 52. |
