A294969 Decimal expansion of sqrt(14)/2 = sqrt(7/2) = A010471/2.

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

Offset: 1

Author

Wolfdieter Lang, Nov 27 2017

Keywords

• nonn
• cons
• easy

Comments

The regular continued fraction of sqrt(14)/2 is [1, repeat(1, 6, 1, 2)].

The convergents are given in A295336/A295337.

sqrt(14)/2 appears in a regular hexagon inscribed in a circle of radius 1 unit in the following way. Draw a straight line through two opposed midpoints of a side (halving the hexagon). The length between one of the midpoints, say M, and one of the two vertices nearest to the opposed midpoint is sqrt(13)/2 = A295330 units. A circle through M with this length ratio sqrt(13)/2 intersects the line below the hexagon at a point, say P. Then the length ratio between P and one of the two vertices nearest to M is sqrt(14)/2 (from a right triangle (1/2, sqrt(13)/2, sqrt(14)/2)).

Examples

			1.87082869338697069279187436615827465087800990388936347315187273366001757815...
		

Crossrefs

Cf. A010471, A295330, A295336/A295337.

Programs

Mathematica

First[RealDigits[Sqrt[14]/2, 10, 100]] (* Paolo Xausa, May 23 2025 *)