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A195348 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(3),2) and vertex angles of degree measure 30,60,90. 3
7, 5, 7, 8, 7, 4, 7, 6, 3, 9, 2, 6, 0, 2, 3, 9, 9, 8, 8, 1, 2, 1, 8, 6, 7, 4, 7, 4, 2, 7, 0, 0, 9, 5, 3, 0, 3, 4, 6, 7, 9, 2, 5, 4, 0, 1, 9, 4, 4, 5, 2, 0, 3, 5, 8, 4, 1, 3, 3, 3, 8, 1, 7, 4, 6, 1, 0, 0, 9, 1, 5, 8, 9, 3, 3, 7, 9, 8, 1, 0, 2, 3, 2, 1, 8, 3, 1, 2, 7, 1, 1, 0, 1, 2, 8, 5, 8, 2, 1, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

See A195284 for definitions and a general discussion.

LINKS

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

EXAMPLE

(A)=0.7578747639260239988121867474270095303467925401944...

(A)=(4*sqrt(6-3*sqrt(3)))/(3+sqrt(3))

(B)=2-(2/3)sqrt(3)

(C)=sqrt(6)-sqrt(2)

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, A093821, A120683, A195380.

Sequence in context: A194657 A230163 A143297 * A072449 A088839 A111769

Adjacent sequences:  A195345 A195346 A195347 * A195349 A195350 A195351

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 17 2011

STATUS

approved

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Last modified July 25 12:01 EDT 2014. Contains 244910 sequences.