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.
101234567817144161178195212229246263280577489654736050662772047781835889359512196011663201859212055222251232447242643252839263035273231286658575649984...
011111111121719212325272931336857764571378184991798510531121231019601219112422126531288413115133461357713808178472665857...

Diophantine equation:s2-72p2 = 1
d = distance to nearest square N2:+8
Smallest non-trivial s:(2*64+8)/8rational: 17actual: 17⇒ F=34
Smallest non-trivial p:2*8/8rational: 2actual: 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.
s11757719601665857...
p0268231078472...

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.


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31323334353738394041424344454647485051525354555657
58596061626365666768697071727374757677787980828384
858687888990919293949596979899101102103104105106107108109110