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A244046
Decimal expansion of the maximal width of a Reuleaux triangle avoiding all vertices of the integer square lattice.
1
1, 5, 4, 4, 9, 4, 1, 7, 0, 0, 3, 7, 1, 5, 9, 3, 1, 5, 4, 1, 8, 5, 0, 9, 6, 8, 3, 8, 4, 7, 0, 6, 2, 6, 5, 8, 0, 2, 4, 7, 3, 6, 0, 8, 2, 8, 4, 0, 0, 6, 7, 4, 1, 7, 4, 0, 8, 0, 5, 1, 5, 9, 4, 9, 4, 3, 7, 0, 0, 9, 9, 5, 7, 4, 2, 3, 0, 0, 6, 9, 8, 6, 0, 6, 6, 9, 0, 7, 3, 8, 5, 0, 8, 0, 6, 1, 7, 9, 7, 3, 6, 3, 9, 3, 7
OFFSET
1,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.10 Reuleaux triangle constants, p. 515.
LINKS
Eric Weisstein's MathWorld, Reuleaux Triangle
FORMULA
Smallest positive root of 4*x^6 - 12*x^5 + x^4 + 22*x^3 - 14*x^2 - 4*x + 4.
EXAMPLE
1.54494170037159315418509683847062658...
MATHEMATICA
w = Root[4*x^6 - 12*x^5 + x^4 + 22*x^3 - 14*x^2 - 4*x + 4, x, 3]; RealDigits[w, 10, 105] // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved