72 is carréphylic - approach of √72=6√2 ~ 8.4852813742
Subsequent approximations of √72 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-72p2 = 1 | | | |
| d = distance to nearest square N2: | +8 | | | |
| Smallest non-trivial s: | (2*64+8)/8 | rational: 17 | actual: 17 | ⇒ F=34 |
| Smallest non-trivial p: | 2*8/8 | rational: 2 | actual: 2 | ⇒ primus foldage=2 |
| v-value qt-blocks: | 82-72*12: | -8 | | |
| Number of series: | 10 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 17 | 577 | 19601 | 665857 | ... |
| p | 0 | 2 | 68 | 2310 | 78472 | ... |
| In the numerator: | U(1,17)34 | = | 1/2*U(2,34)34 | - | half the secundus of 34. |
| In the denominator: | U(0,2)34 | = | 2*U(0,1)34 | - | the 2-fold primus of 34. |
| as well as ... |
| In the numerator: | U(0,144)34 | = | 144*U(0,1)34 | - | the 72*2-fold primus of 34. |
| In the denominator: | U(1,17)34 | = | 1/2*U(2,34)34 | - | half the secundus of 34. |
| and ... |
| In the numerator: | U(-8,8)34 | = | 8*U(-1,1)34 | - | the 8-fold quartus of 34. |
| In the denominator: | U(1,1)34 | = | | - | the tertius of 34. |
