55 is carréphobic - approach of √55 ~ 7.4161984871

Subsequent approximations of √55 - the position of a fraction indicates whether it is over or under the root-value.
101234567152237528966074983892710161105119412832655393865939248158411174801333211491621650031808441966852125262283674725757009421173517164609228196092091078023730389265499982936960732189216350088253782843440648043841156951247637382088794332929951285018745613722001360...
011111111235712891011131251371491611733585318891247213615841179772011322249243852652128657307936372294515158237221959380196281960931998053580001396019743403934720589510078554809811134215816823139281652973950745567672752501874561...

Diophantine equation:s2-55p2 = 1
d = distance to nearest square N2:+6
Smallest non-trivial s:(2*49+6)/6rational: 104/6actual: 89⇒ F=178
Smallest non-trivial p:2*7/6rational: 14/6actual: 12⇒ primus foldage=12
v-value tq-blocks:152-55*22:+5
v-value qt-blocks:222-55*32:-11
Number of series:13

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
...
s189158412819609501874561
p012213638019667672752...

In the numerator:U(1,89)178=1/2*U(2,178)178-half the secundus of 178.
In the denominator:U(0,12)178=12*U(0,1)178-the 12-fold primus of 178.
as well as ...
In the numerator:U(0,660)178=660*U(0,1)178-the 55*12-fold primus of 178.
In the denominator:U(1,89)178=1/2*U(2,178)178-half the secundus of 178.
and ...
In the numerator:U(15,15)178=15*U(1,1)178-the 15-fold tertius of 178.
In the denominator:U(-2,2)178=2*U(-1,1)178-the 2-fold quartus of 178.
and ...
In the numerator:U(-22,22)178=22*U(-1,1)178-the 22-fold quartus of 178.
In the denominator:U(3,3)178=3*U(1,1)178-the 3-fold tertius of 178.


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31323334353738394041424344454647485051525354555657
58596061626365666768697071727374757677787980828384
858687888990919293949596979899101102103104105106107108109110