95 is carréphylic - approach of √95 ~ 9.7467943448
Subsequent approximations of √95 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-95p2 = 1 | | | |
| d = distance to nearest square N2: | -5 | | | |
| Smallest non-trivial s: | (2*100-5)/5 | rational: 39 | actual: 39 | ⇒ F=78 |
| Smallest non-trivial p: | 2*10/5 | rational: 4 | actual: 4 | ⇒ primus foldage=4 |
| v-value t/q-fraction: | 102-95*12: | +5 | | |
| v-value q/t-fraction: | 192-95*22: | -19 | | |
| Number of series: | 14 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| In the numerator: | U(1,39)78 | = | 1/2*U(2,78)78 | - | half the secundus of 78. |
| In the denominator: | U(0,4)78 | = | 4*U(0,1)78 | - | the 4-fold primus of 78. |
| as well as ... |
| In the numerator: | U(0,380)78 | = | 380*U(0,1)78 | - | the 95*4-fold primus of 78. |
| In the denominator: | U(1,39)78 | = | 1/2*U(2,78)78 | - | half the secundus of 78. |
| and ... |
| In the numerator: | U(10,10)78 | = | 10*U(1,1)78 | - | the 10-fold tertius of 78. |
| In the denominator: | U(-1,1)78 | = | | - | the quartus of 78. |
| and ... |
| In the numerator: | U(-19,19)78 | = | 19*U(-1,1)78 | - | the 19-fold quartus of 78. |
| In the denominator: | U(2,2)78 | = | 2*U(1,1)78 | - | the 2-fold tertius of 78. |
