33 is carréphylic - approach of √33 ~ 5.7445626465
Subsequent approximations of √33 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-33p2 = 1 | | | |
| d = distance to nearest square N2: | -3 | | | |
| Smallest non-trivial s: | (2*36-3)/3 | rational: 23 | actual: 23 | ⇒ F=46 |
| Smallest non-trivial p: | 2*6/3 | rational: 4 | actual: 4 | ⇒ primus foldage=4 |
| v-value tq-blocks: | 62-33*12: | +3 | | |
| v-value qt-blocks: | 112-33*22: | -11 | | |
| Number of series: | 10 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 23 | 1057 | 48599 | 2234497 | 102738263 | ... |
| p | 0 | 4 | 184 | 8460 | 388976 | 17884436 | ... |
| In the numerator: | U(1,23)46 | = | 1/2*U(2,46)46 | - | half the secundus of 46. |
| In the denominator: | U(0,4)46 | = | 4*U(0,1)46 | - | the 4-fold primus of 46. |
| as well as ... |
| In the numerator: | U(0,132)46 | = | 132*U(0,1)46 | - | the 33*4-fold primus of 46. |
| In the denominator: | U(1,23)46 | = | 1/2*U(2,46)46 | - | half the secundus of 46. |
| and ... |
| In the numerator: | U(6,6)46 | = | 6*U(1,1)46 | - | the 6-fold tertius of 46. |
| In the denominator: | U(-1,1)46 | = | | - | the quartus of 46. |
| and ... |
| In the numerator: | U(-11,11)46 | = | 11*U(-1,1)46 | - | the 11-fold quartus of 46. |
| In the denominator: | U(2,2)46 | = | 2*U(1,1)46 | - | the 2-fold tertius of 46. |
