OFFSET
1,2
COMMENTS
The regular continued fraction of sqrt(14)/2 is [1, repeat(1, 6, 1, 2)].
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 rectangular triangle (1/2, sqrt(13)/2, sqrt(14)/2).
EXAMPLE
1.87082869338697069279187436615827465087800990388936347315187273366001757815...
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Wolfdieter Lang, Nov 27 2017
STATUS
approved