28 is carréphobic - approach of √28=2√7 ~ 5.2915026221
Subsequent approximations of √28 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-28p2 = 1 | | | |
| d = distance to nearest square N2: | +3 | | | |
| Smallest non-trivial s: | (2*25+3)/3 | rational: 53/3 | actual: 127 | ⇒ F=254 |
| Smallest non-trivial p: | 2*5/3 | rational: 10/3 | actual: 24 | ⇒ primus foldage=24 |
| v-value tq-blocks: | 162-28*32: | +4 | | |
| v-value qt-blocks: | 212-28*42: | -7 | | |
| Number of series: | 12 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 127 | 32257 | 8193151 | ... |
| p | 0 | 24 | 6096 | 1548360 | ... |
| In the numerator: | U(1,127)254 | = | 1/2*U(2,254)254 | - | half the secundus of 254. |
| In the denominator: | U(0,24)254 | = | 24*U(0,1)254 | - | the 24-fold primus of 254. |
| as well as ... |
| In the numerator: | U(0,672)254 | = | 672*U(0,1)254 | - | the 28*24-fold primus of 254. |
| In the denominator: | U(1,127)254 | = | 1/2*U(2,254)254 | - | half the secundus of 254. |
| and ... |
| In the numerator: | U(16,16)254 | = | 16*U(1,1)254 | - | the 16-fold tertius of 254. |
| In the denominator: | U(-3,3)254 | = | 3*U(-1,1)254 | - | the 3-fold quartus of 254. |
| and ... |
| In the numerator: | U(-21,21)254 | = | 21*U(-1,1)254 | - | the 21-fold quartus of 254. |
| In the denominator: | U(4,4)254 | = | 4*U(1,1)254 | - | the 4-fold tertius of 254. |
Note: 28 is carréphobic, but has
carréphylic ancestry.
