94 is carréphobic - approach of √94 ~ 9.6953597148
Using the
incremental profile, the questionmarks can be filled in - the position of a fraction indicates whether it is over or under the root-value. The positioning of the missing fractions corresponds to the first section.
Subsequent approximations of √94.
| Diophantine equation: | s2-94p2 = 1 | | | |
| d = distance to nearest square N2: | -6 | | | |
| Smallest non-trivial s: | (2*100-6)/6 | rational: 194/6 | actual: 2143295 | ⇒ F=4286590 |
| Smallest non-trivial p: | 2*10/6 | rational: 20/6 | actual: 221064 | ⇒ primus foldage=221064 |
| v-value tq-blocks: | 14642-94*1512: | +2 | | |
| v-value qt-blocks: | 70972-94*7322: | -47 | | |
| Number of series: | 36 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 2143295 | 9187426914049 | ... |
| p | 0 | 221064 | 947610731760 | ... |
| In the numerator: | U(1,2143295)4286590 | = | 1/2*U(2,4286590)4286590 | - | half the secundus of 4286590. |
| In the denominator: | U(0,221064)4286590 | = | 221064*U(0,1)4286590 | - | the 221064-fold primus of 4286590. |
| as well as ... |
| In the numerator: | U(0,20780016)4286590 | = | 20780016*U(0,1)4286590 | - | the 94*221064-fold primus of 4286590. |
| In the denominator: | U(1,2143295)4286590 | = | 1/2*U(2,4286590)4286590 | - | half the secundus of 4286590. |
| and ... |
| In the numerator: | U(1464,1464)4286590 | = | 1464*U(1,1)4286590 | - | the 1464-fold tertius of 4286590. |
| In the denominator: | U(-151,151)4286590 | = | 151*U(-1,1)4286590 | - | the 151-fold quartus of 4286590. |
| and ... |
| In the numerator: | U(-7097,7097)4286590 | = | 7097*U(-1,1)4286590 | - | the 7097-fold quartus of 4286590. |
| In the denominator: | U(732,732)4286590 | = | 732*U(1,1)4286590 | - | the 732-fold tertius of 4286590. |
