A195409 Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(r-1,r,sqrt(3)), where r=(1+sqrt(5))/2 (the golden ratio).

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

Offset

0,1

Comments

See A195284 for definitions and a general discussion.

Links

Table of n, a(n) for n=0..103.

Example

(C)=0.71278791738520123380160946972682714175360765866...

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.

Sequence in context: A155773 A215670 A010144 * A318353 A354639 A273984

Adjacent sequences: A195406 A195407 A195408 * A195410 A195411 A195412

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Extensions

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

Status

approved