10 is carréphylic - approach of √10 ~ 3.1622776602
Subsequent approximations of √10 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-10p2 = 1 | | | |
| d = distance to nearest square N2: | +1 | | | |
| Smallest non-trivial s: | (2*9+1)/1 | rational: 19 | actual: 19 | ⇒ F=38 |
| Smallest non-trivial p: | 2*3/1 | rational: 6 | actual: 6 | ⇒ primus foldage=6 |
| v-value qt-blocks: | 32-10*12: | -1 | | |
| Number of series: | 7 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 19 | 721 | 27379 | 1039681 | 39480499 | ... |
| p | 0 | 6 | 228 | 8658 | 328776 | 12484830 | ... |
| In the numerator: | U(1,19)38 | = | 1/2*U(2,38)38 | - | half the secundus of 38. |
| In the denominator: | U(0,6)38 | = | 6*U(0,1)38 | - | the 6-fold primus of 38. |
| as well as ... |
| In the numerator: | U(0,60)38 | = | 60*U(0,1)38 | - | the 10*6-fold primus of 38. |
| In the denominator: | U(1,19)38 | = | 1/2*U(2,38)38 | - | half the secundus of 38. |
| and ... |
| In the numerator: | U(-3,3)38 | = | 3*U(-1,1)38 | - | the 3-fold quartus of 38. |
| In the denominator: | U(1,1)38 | = | | - | the tertius of 38. |
