44 is carréphobic - approach of √44=2√11 ~ 6.6332495807
Subsequent approximations of √44 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-44p2 = 1 | | | |
| d = distance to nearest square N2: | -5 | | | |
| Smallest non-trivial s: | (2*49-5)/5 | rational: 93/5 | actual: 199 | ⇒ F=398 |
| Smallest non-trivial p: | 2*7/5 | rational: 14/5 | actual: 30 | ⇒ primus foldage=30 |
| v-value tq-blocks: | 202-44*32: | +4 | | |
| v-value qt-blocks: | 332-44*52: | -11 | | |
| Number of series: | 15 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 199 | 79201 | 31521799 | ... |
| p | 0 | 30 | 11940 | 4752090 | ...... |
| In the numerator: | U(1,199)398 | = | 1/2*U(2,398)398 | - | half the secundus of 398. |
| In the denominator: | U(0,30)398 | = | 30*U(0,1)398 | - | the 30-fold primus of 398. |
| as well as ... |
| In the numerator: | U(0,1320)398 | = | 1320*U(0,1)398 | - | the 44*30-fold primus of 398. |
| In the denominator: | U(1,199)398 | = | 1/2*U(2,398)398 | - | half the secundus of 398. |
| and ... |
| In the numerator: | U(20,20)398 | = | 20*U(1,1)398 | - | the 20-fold tertius of 398. |
| In the denominator: | U(-3,3)398 | = | 3*U(-1,1)398 | - | the 3-fold quartus of 398. |
| and ... |
| In the numerator: | U(-33,33)398 | = | 33*U(-1,1)398 | - | the 33-fold quartus of 398. |
| In the denominator: | U(5,5)398 | = | 5*U(1,1)398 | - | the 5-fold tertius of 398. |
