A195348 Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(3),2) and vertex angles of degree measure 30,60,90.

7, 5, 7, 8, 7, 4, 7, 6, 3, 9, 2, 6, 0, 2, 3, 9, 9, 8, 8, 1, 2, 1, 8, 6, 7, 4, 7, 4, 2, 7, 0, 0, 9, 5, 3, 0, 3, 4, 6, 7, 9, 2, 5, 4, 0, 1, 9, 4, 4, 5, 2, 0, 3, 5, 8, 4, 1, 3, 3, 3, 8, 1, 7, 4, 6, 1, 0, 0, 9, 1, 5, 8, 9, 3, 3, 7, 9, 8, 1, 0, 2, 3, 2, 1, 8, 3, 1, 2, 7, 1, 1, 0, 1, 2, 8, 5, 8, 2, 1, 3

Offset

0,1

Comments

See A195284 for definitions and a general discussion.

Links

Table of n, a(n) for n=0..99.

Example

(A)=0.7578747639260239988121867474270095303467925401944...
(A)=(4*sqrt(6-3*sqrt(3)))/(3+sqrt(3))
(B)=2-(2/3)sqrt(3)
(C)=sqrt(6)-sqrt(2)

Mathematica

a = 1; b = Sqrt[3]; c = 2;
f = 2 a*b/(a + b + c);
x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
x3 = f*Sqrt[2]
N[x1, 100]
RealDigits[%] (* (A) A195348 *)
N[x2, 100]
RealDigits[%] (* (B) A093821 *)
N[x3, 100]
RealDigits[%] (* (C) A120683 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* A195380 *)

Crossrefs

Cf. A195284, A093821, A120683, A195380.

Sequence in context: A194657 A230163 A143297 * A072449 A263770 A088839

Adjacent sequences: A195345 A195346 A195347 * A195349 A195350 A195351

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Status

approved