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A195692 Decimal expansion of arccos(1/phi), where phi = (1+sqrt(5))/2 (the golden ratio). 4
9, 0, 4, 5, 5, 6, 8, 9, 4, 3, 0, 2, 3, 8, 1, 3, 6, 4, 1, 2, 7, 3, 1, 6, 7, 9, 5, 6, 6, 1, 9, 5, 8, 7, 2, 1, 4, 3, 1, 0, 9, 4, 5, 6, 0, 9, 6, 1, 6, 0, 5, 0, 6, 7, 6, 5, 5, 9, 9, 8, 4, 5, 3, 3, 4, 9, 9, 2, 9, 2, 1, 3, 7, 6, 4, 0, 4, 5, 2, 1, 7, 6, 0, 6, 1, 1, 0, 5, 8, 1, 5, 0, 1, 4, 7, 7, 3, 9, 8, 7, 3, 1, 2, 9, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Every cyclic quadrilateral all of whose angles are greater than arccos((sqrt(5)-1)/2) admits a 3 × 1 grid dissection into three cyclic quadrilaterals [Thm. 2.3 in Choi et al. p. 2]. - Michel Marcus, Aug 13 2019

LINKS

Table of n, a(n) for n=0..104.

Erica Choi, Dan Ismailescu, Jiho Lee, Joonsoo Lee, Grid dissections of tangential quadrilaterals, arXiv:1908.02251 [math.MG], 2019.

EXAMPLE

arccos(1/r) = 0.904556894302381364127316795661958721...

cos(0.904556894302381364127316795661958721...) = 1/(golden ratio) = 0.618...

sec(0.904556894302381364127316795661958721...) = (golden ratio) = 1.618...

MATHEMATICA

r = 1/GoldenRatio;

N[ArcSin[r], 100]

RealDigits[%]  (* A175288, =ArcCsc[GoldenRatio]] *)

N[ArcCos[r], 100]

RealDigits[%]  (* A195692 *)

N[ArcTan[r], 100]

RealDigits[%]  (* A195693 *)

N[ArcCos[-r], 100]

RealDigits[%]  (* A195694 *)

CROSSREFS

Cf. A001622, A175288, A195693, A195694.

Sequence in context: A215141 A248951 A198226 * A021088 A021529 A196398

Adjacent sequences:  A195689 A195690 A195691 * A195693 A195694 A195695

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 22 2011

EXTENSIONS

Terms replaced with intended terms by Rick L. Shepherd, Jan 30 2013

STATUS

approved

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Last modified December 15 03:48 EST 2019. Contains 329990 sequences. (Running on oeis4.)