51 is carréphylic - approach of √51 ~ 7.1414284285
Subsequent approximations of √51 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-51p2 = 1 | | | |
| d = distance to nearest square N2: | +2 | | | |
| Smallest non-trivial s: | (2*49+2)/2 | rational: 50 | actual: 50 | ⇒ F=100 |
| Smallest non-trivial p: | 2*7/2 | rational: 7 | actual: 7 | ⇒ primus foldage=7 |
| v-value qt-blocks: | 72-51*12: | -2 | | |
| Number of series: | 12 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 50 | 4999 | 499850 | 49980001 | ... |
| p | 0 | 7 | 700 | 69993 | 6998600 | ... |
| In the numerator: | U(1,50)100 | = | 1/2*U(2,100)100 | - | half the secundus of 100. |
| In the denominator: | U(0,7)100 | = | 7*U(0,1)100 | - | the 7-fold primus of 100. |
| as well as ... |
| In the numerator: | U(0,357)100 | = | 357*U(0,1)100 | - | the 51*7-fold primus of 100. |
| In the denominator: | U(1,50)100 | = | 1/2*U(2,100)100 | - | half the secundus of 100. |
| and ... |
| In the numerator: | U(-7,7)100 | = | 7*U(-1,1)100 | - | the 7-fold quartus of 100. |
| In the denominator: | U(1,1)100 | = | | - | the tertius of 100. |
