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 A188544 Decimal expansion of the angle B in the doubly e-ratio triangle ABC. 2
 3, 6, 8, 9, 3, 1, 2, 7, 4, 9, 4, 7, 8, 0, 5, 8, 4, 2, 6, 5, 1, 9, 1, 1, 2, 7, 2, 6, 8, 8, 6, 4, 0, 8, 5, 7, 1, 8, 6, 8, 3, 4, 4, 2, 8, 8, 3, 5, 2, 6, 1, 9, 0, 6, 5, 9, 8, 5, 4, 6, 2, 1, 2, 1, 1, 1, 1, 7, 6, 5, 9, 8, 7, 5, 6, 8, 4, 9, 0, 6, 0, 6, 7, 0, 1, 2, 1, 0, 6, 0, 4, 8, 5, 9, 8, 4, 2, 8, 4, 2, 8, 0, 9, 9, 1, 1, 8, 2, 1, 8, 8, 5, 9, 6, 9, 8, 4, 4, 2, 2, 9, 4, 8, 7, 3, 4, 6, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS There is a unique (shape of) triangle ABC that is both side-e-ratio and angle-e-ratio. Its angles are B, t*B and pi-B-t*B, where t=e. "Side-e-ratio" and "angle-e-ratio" refer to partitionings of ABC, each in a manner that matches the continued fraction [2,1,2,1,1,4,1,1,6,...] of t.  For doubly golden and doubly silver triangles, see A152149 and A188543.  For the side partitioning and angle partitioning (i,e, constructions) which match arbitrary continued fractions (of sidelength ratios and angle ratios), see the 2007 reference. LINKS Clark Kimberling, Two kinds of golden triangles, generalized to match continued fractions, Journal for Geometry and Graphics, 11 (2007) 165-171. FORMULA B is the number in [0,Pi] such that sin(B*e^2)=e*sin(B). EXAMPLE B=0.36893127494780584265191127268864 approximately. B=21.1382 degrees approximately. MATHEMATICA r = E; Clear[t]; RealDigits[FindRoot[Sin[r*t + t] == r*Sin[t], {t, 1}, WorkingPrecision -> 120][[1, 2]]][[1]] CROSSREFS Cf. A152149, A188543. Sequence in context: A016663 A023993 A133159 * A163463 A137386 A153307 Adjacent sequences:  A188541 A188542 A188543 * A188545 A188546 A188547 KEYWORD nonn,cons AUTHOR Clark Kimberling, Apr 03 2011 STATUS approved

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Last modified July 21 00:49 EDT 2019. Contains 325189 sequences. (Running on oeis4.)