A070200 Inradii of integer triangles [A070080(n), A070081(n), A070082(n)], rounded values.

0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2

Offset: 1

Author

Reinhard Zumkeller, May 05 2002

Keywords

• nonn

Comments

Triangles [A070080(A070209(n)), A070081(A070209(n)), A070082(A070209(n))] have integer inradii = a(A070209(k))= A070210(k).

Examples

			[A070080(25), A070081(25), A070082(25)] = [3,5,6] and s = A070083(25)/2 = (3+5+6)/2 = 7: a(25) = sqrt((s-3)*(s-5)*(s-6)/7) = sqrt((7-3)*(7-5)*(7-6)/7) = sqrt(4*2*1/7) = sqrt(8/7) = 1.069, rounded = 1.
		

Links

• Eric Weisstein's World of Mathematics, Incircle.
• R. Zumkeller, Integer-sided triangles

Crossrefs

Cf. A070086.

Formula

a(n) = sqrt((s-u)*(s-v)*(s-w)/s), where u=A070080(n), v=A070081(n), w=A070082(n) and s=A070083(n)/2=(u+v+w)/2.