A195380 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 1,sqrt(3),sqrt(1) right triangle ABC (angles 30, 60, 90).

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

Offset

0,1

Comments

See A195284 for definitions and a general discussion.

Links

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

Example

Philo(ABC,I)=0.55757017691709380372112914604292318...

Mathematica

a = 1; b = Sqrt[3]; c = 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) A195348 *)
N[x2, 100]
RealDigits[%] (* (B) A093821 *)
N[x3, 100]
RealDigits[%] (* (C) A120683 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* A195380 *)

Crossrefs

Cf. A195284.

Sequence in context: A052247 A088201 A352353 * A139261 A352442 A247649

Adjacent sequences: A195377 A195378 A195379 * A195381 A195382 A195383

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Status

approved