A128006 Numerators of rational-valued radii of circles given by 3 distinct integer points in the euclidean plane.

1, 5, 5, 2, 17, 13, 5, 13, 29, 3, 37, 25, 13, 10, 17, 25, 15, 53, 65, 4, 65, 41, 29, 25, 17, 13, 41, 73, 65, 85, 5, 101, 61, 41, 26, 37, 85, 97, 65, 109, 61, 89, 325, 17, 125, 29, 53, 65, 6, 145, 85, 61, 37, 137, 25, 51, 13, 85, 205, 73, 173, 533, 20, 34, 89, 7, 197, 169, 113, 85

Offset: 1

Author

Heinrich Ludwig, Feb 11 2007

Keywords

• frac
• nonn

Comments

A triangle in the Euclidean plane defines a circumcircle. There exist only certain rational-valued circumradii if the vertices of the triangle have integer coordinates. They are rendered by the pair of sequences A128006/A128007 in increasing order.

Links

• Illustration of A128006/A128007 using Plot 2.

Crossrefs

See A128007 for denominators.

Cf. A128008, A128009, A128010, A128011, A192493, A192494.