A386241 Decimal expansion of sqrt(5)*sin(Pi/8).

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

Offset: 0

Author

Hugo Pfoertner, Jul 18 2025

Keywords

• nonn
• cons
• changed

Comments

Upper bound of the wobbling distance S of two rotated square lattices. See A307110 and A307731 for the special case of rotation angle Pi/4. According to Jan Fricke (1999), the angle Pi/4 is the most unfavorable case, i.e., smaller bounds can be found for all other angles.

Examples

			0.8557061686312838477748180718246837073...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Hans-Georg Carstens, Walter A. Deuber, Wolfgang Thumser, and Elke Koppenrade, Geometrical Bijections in Discrete Lattices. Combinatorics, Probability and Computing, 8(1-2), 109-129, 1999.
• Jan Fricke, Symmetric Graphs have symmetric Matchings, arXiv:1607.07426 [math.GR], 25 Jul 2016, Introduction.
• Klaus Nagel, A Lower Bound for Double Lattice Bijections, August 17, 2025.
• Index entries for algebraic numbers, degree 4

Crossrefs

Cf. A002163, A144981, A182168, A307110, A307731, A367150.

Programs

Mathematica

First[RealDigits[Sqrt[5]*Sin[Pi/8],10,100]] (* Paolo Xausa, Aug 13 2025 *)

PARI

sqrt(5)*sin(Pi/8) \\ Charles R Greathouse IV, Aug 19 2025

Formula

Equals A002163*A182168.

The minimal polynomial is 8*x^4 - 40*x^2 + 25. - Joerg Arndt, Aug 02 2025