47 is carréphylic - approach of √47 ~ 6.8556546004
Subsequent approximations of √47 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-47p2 = 1 | | | |
| d = distance to nearest square N2: | -2 | | | |
| Smallest non-trivial s: | (2*49-2)/2 | rational: 48 | actual: 48 | ⇒ F=96 |
| Smallest non-trivial p: | 2*7/2 | rational: 7 | actual: 7 | ⇒ primus foldage=7 |
| v-value tq-blocks: | 72-47*12: | +2 | | |
| Number of series: | 12 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 48 | 4607 | 442224 | 42448897 | ... |
| p | 0 | 7 | 672 | 64505 | 6191808 | ... |
| In the numerator: | U(1,48)96 | = | 1/2*U(2,96)96 | - | half the secundus of 96. |
| In the denominator: | U(0,7)96 | = | 7*U(0,1)96 | - | the 7-fold primus of 96. |
| as well as ... |
| In the numerator: | U(0,329)96 | = | 329*U(0,1)96 | - | the 47*7-fold primus of 96. |
| In the denominator: | U(1,48)96 | = | 1/2*U(2,96)96 | - | half the secundus of 96. |
| and ... |
| In the numerator: | U(7,7)96 | = | 7*U(1,1)96 | - | the 7-fold tertius of 96. |
| In the denominator: | U(-1,1)96 | = | | - | the quartus of 96. |
