A195407 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)=(r-1,r,sqrt(3)), where r=(1+sqrt(5))/2 (the golden ratio).

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

Offset

0,1

Comments

See A195284 for definitions and a general discussion.

Links

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

Example

(A)=0.51252227236222537926354945581073551694...

Mathematica

a = b - 1; b = (1 + Sqrt[5])/2; c = Sqrt[3];
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) A195407 *)
N[x2, 100]
RealDigits[%]    (* (B) A195408 *)
N[x3, 100]
RealDigits[%]    (* (C) A195409 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC, I) A195410 *)

Crossrefs

Cf. A195284, A195408, A195409, A195410.

Sequence in context: A157823 A159703 A059521 * A011509 A361970 A144738

Adjacent sequences: A195404 A195405 A195406 * A195408 A195409 A195410

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Status

approved