52 is carréphobic - approach of √52 ~ 7.2111025509
Subsequent approximations of √52 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-52p2 = 1 | | | |
| d = distance to nearest square N2: | +3 | | | |
| Smallest non-trivial s: | (2*49+3)/3 | rational: 101/3 | actual: 649 | ⇒ F=1298 |
| Smallest non-trivial p: | 2*7/3 | rational: 14/3 | actual: 90 | ⇒ primus foldage=90 |
| v-value qt-blocks: | 362-52*52: | -4 | | |
| Number of series: | 16 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 649 | 842401 | 1093435846 | ... |
| p | 0 | 90 | 116820 | 151632270 | ... |
| In the numerator: | U(1,649)1298 | = | 1/2*U(2,1298)1298 | - | half the secundus of 1298. |
| In the denominator: | U(0,90)1298 | = | 90*U(0,1)1298 | - | the 90-fold primus of 1298. |
| as well as ... |
| In the numerator: | U(0,4680)1298 | = | 4680*U(0,1)1298 | - | the 52*90-fold primus of 1298. |
| In the denominator: | U(1,649)1298 | = | 1/2*U(2,1298)1298 | - | half the secundus of 1298. |
| and ... |
| In the numerator: | U(-36,36)1298 | = | 36*U(-1,1)1298 | - | the 36-fold quartus of 1298. |
| In the denominator: | U(5,5)1298 | = | 5*U(1,1)1298 | - | the 5-fold tertius of 1298. |
