A195395 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)=(sqrt(3),sqrt(5),sqrt(8)).

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

Offset

1,2

Comments

See A195284 for definitions and a general discussion.

Links

Table of n, a(n) for n=1..100.

Index entries for algebraic numbers, degree 10

Example

(A)=1.204499952438300422962677204955880425372499...

Mathematica

a = Sqrt[3]; b = Sqrt[5]; c = Sqrt[8];
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) A195395 *)
N[x2, 100]
RealDigits[%]    (* (B) A195396 *)
N[x3, 100]
RealDigits[%]    (* (C) A195397 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC, I) A195398 *)

Prog

(PARI) 4*sqrt(15*sqrt(10)+60)/(sqrt(15)+2*sqrt(6)+4*sqrt(10)+13) \\ Charles R Greathouse IV, Apr 07 2026
(PARI) polrootsreal(9*x^10 - 4983*x^8 + 452992*x^6 - 2736896*x^4 + 491520*x^2 + 3686400)[5] \\ Charles R Greathouse IV, Apr 07 2026

Crossrefs

Cf. A195284, A195896, A195897, A195398.

Sequence in context: A304877 A147980 A021493 * A390568 A296805 A336974

Adjacent sequences: A195392 A195393 A195394 * A195396 A195397 A195398

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Status

approved