60 is carréphylic - approach of √60=2√15 ~ 7.7459666924
Subsequent approximations of √60 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-60p2 = 1 | | | |
| d = distance to nearest square N2: | -4 | | | |
| Smallest non-trivial s: | (2*64-4)/4 | rational: 31 | actual: 31 | ⇒ F=62 |
| Smallest non-trivial p: | 2*8/4 | rational: 4 | actual: 4 | ⇒ primus foldage=4 |
| v-value t/q-fraction: | 82-60*12: | +4 | | |
| v-value q/t-fraction: | 152-60*22: | -15 | | |
| Number of series: | 12 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 31 | 1921 | 119071 | 7380481 | 457470751 | ... |
| p | 0 | 4 | 248 | 15372 | 952816 | 59059220 | ... |
| In the numerator: | U(1,31)62 | = | 1/2*U(2,62)62 | - | half the secundus of 62. |
| In the denominator: | U(0,4)62 | = | 4*U(0,1)62 | - | the 4-fold primus of 62. |
| as well as ... |
| In the numerator: | U(0,240)62 | = | 240*U(0,1)62 | - | the 60*4-fold primus of 62. |
| In the denominator: | U(1,31)62 | = | 1/2*U(2,62)62 | - | half the secundus of 62. |
| and ... |
| In the numerator: | U(8,8)62 | = | 8*U(1,1)62 | - | the 8-fold tertius of 62. |
| In the denominator: | U(-1,1)62 | = | | - | the quartus of 62. |
| and ... |
| In the numerator: | U(-15,15)62 | = | 15*U(-1,1)62 | - | the 15-fold quartus of 62. |
| In the denominator: | U(2,2)62 | = | 2*U(1,1)62 | - | the 2-fold tertius of 62. |
