A195403 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(r),r), where r=(1+sqrt(5))/2 (the golden ratio).

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

Offset: 0

Author

Clark Kimberling, Sep 17 2011

Keywords

• nonn
• cons

Comments

See A195284 for definitions and a general discussion.

Examples

			(A)=0.69202867847165176790432874525629325200...
		

Crossrefs

Cf. A195284, A195404, A195405, A195406.

Programs

Mathematica

a = 1; b = Sqrt[c]; c = (1 + Sqrt[5])/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) A195403 *)
N[x2, 100]
RealDigits[%]    (* (B) A195404 *)
N[x3, 100]
RealDigits[%]    (* (C) A195405 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC,I) A195406 *)

Extensions

a(99) corrected by Georg Fischer, Jul 18 2021