22 is carréphobic - approach of √22 ~ 4.6904157598
Subsequent approximations of √22 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-22p2 = 1 | | | |
| d = distance to nearest square N2: | -3 | | | |
| Smallest non-trivial s: | (2*25-3)/3 | rational: 47/3 | actual: 197 | ⇒ F=394 |
| Smallest non-trivial p: | 2*5/3 | rational: 10/3 | actual: 42 | ⇒ primus foldage=42 |
| v-value qt-blocks: | 142-22*32: | -2 | | |
| Number of series: | 12 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 197 | 77617 | 30580901 | ... |
| p | 0 | 42 | 16548 | 6519870 | ... |
| In the numerator: | U(1,197)394 | = | 1/2*U(2,394)394 | - | half the secundus of 394. |
| In the denominator: | U(0,42)394 | = | 42*U(0,1)394 | - | the 42-fold primus of 394. |
| as well as ... |
| In the numerator: | U(0,924)394 | = | 924*U(0,1)394 | - | the 22*42-fold primus of 394. |
| In the denominator: | U(1,197)394 | = | 1/2*U(2,394)394 | - | half the secundus of 394. |
| and ... |
| In the numerator: | U(-14,14)394 | = | 14*U(-1,1)394 | - | the 14-fold quartus of 394. |
| In the denominator: | U(3,3)394 | = | 3*U(1,1)394 | - | the 3-fold tertius of 394. |
