

A265189


Soddy circles: the two circles tangent to each of three mutually tangent circles.


3



69, 46, 23, 6, 138, 70, 30, 21, 5, 105, 132, 33, 11, 4, 132, 138, 92, 46, 12, 276, 140, 60, 42, 10, 210, 153, 136, 72, 17, 306, 207, 138, 69, 18, 414, 210, 90, 63, 15, 315, 216, 135, 24, 10, 135, 238, 119, 102, 21, 357, 252, 63, 28, 9, 0
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OFFSET

1,1


COMMENTS

For any three mutually tangent circles (with radii a, b, and c), one can construct a fourth circle (the inner Soddy circle, with radius d) that is mutually tangent internally to the three circles, and a fifth circle (the outer Soddy circle, with radius e) that is mutually tangent externally to the three circles. For this sequence all five radii have integral lengths.
The sequence is an array of 5tuples (a,b,c,d,e) ordered by increasing values of a, with a > b > c.
A positive value for the outer Soddy circle indicates that it contains the three circles; a negative value indicates that it is exterior to the three circles; a value of 0 indicates that it has an infinite radius, that is, it is a straight line.


LINKS



PROG

(PARI)
soddy(amax) = {
my(L=List(), abc, t, u);
for(a=1, amax,
for(b=1, a1,
for(c=1, b1,
abc=a*b*c;
if(issquare(abc*(a+b+c), &t),
u=a*b+a*c+b*c;
if(abc%(u+2*t) == 0,
if(u2*t != 0,
if(abc%(u2*t) == 0,
listput(L, [a, b, c, abc\(u+2*t), abc\(u2*t)])
)
,
listput(L, [a, b, c, abc\(u+2*t), 0])
)
)
)
)
)
);
Vec(L)
}
soddy(253)


CROSSREFS



KEYWORD

sign,tabf


AUTHOR



STATUS

approved



