A195405 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)=(1,sqrt(r),r), where r=(1+sqrt(5))/2 (the golden ratio).

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

Offset

0,1

Comments

See A195284 for definitions and a general discussion.

Links

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

Example

(C)=0.92487539105022513066262517351274541075260...

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 *)

Crossrefs

Cf. A195284.

Sequence in context: A020784 A111188 A334845 * A089065 A248319 A154398

Adjacent sequences: A195402 A195403 A195404 * A195406 A195407 A195408

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Status

approved