87 is carréphylic - approach of √87 ~ 9.3273790531
Subsequent approximations of √87 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-87p2 = 1 | | | |
| d = distance to nearest square N2: | +6 | | | |
| Smallest non-trivial s: | (2*81+6)/6 | rational: 28 | actual: 28 | ⇒ F=56 |
| Smallest non-trivial p: | 2*9/6 | rational: 13 | actual: 3 | ⇒ primus foldage=3 |
| v-value qt-blocks: | 92-87*12: | -6 | | |
| Number of series: | 12 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| In the numerator: | U(1,28)56 | = | 1/2*U(2,56)56 | - | half the secundus of 56. |
| In the denominator: | U(0,3)56 | = | 3*U(0,1)56 | - | the 3-fold primus of 56. |
| as well as ... |
| In the numerator: | U(0,261)56 | = | 261*U(0,1)56 | - | the 87*3-fold primus of 56. |
| In the denominator: | U(1,28)56 | = | 1/2*U(2,56)56 | - | half the secundus of 56. |
| and ... |
| In the numerator: | U(-9,9)56 | = | 9*U(-1,1)56 | - | the 9-fold quartus of 56. |
| In the denominator: | U(1,1)56 | = | | - | the tertius of 56. |
