Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
editing
approved
Geometric Interpretation: Given an n-sided regular polygon "rolling" on a flat surface with constant angular velocity, a(n) is the denominator of the ratio: [("time" taken for any one vertex to move from highest point to lowest point) / ("time" taken for polygon to finish one complete turn)] := b(n).
proposed
editing
editing
proposed
Luca Alexander, <a href="/A328184/a328184.txt">about 100000 terms</a>
nonn,frac,more,changed
proposed
editing
editing
proposed
Geometric Interpretation: Given an n-sided regular polygon "rolling" on a flat surface with constant angular velocity, a(n) is the denominator of the ratio: [("time" taken for any one vertex to move from highest point to lowest point) / ("time" taken for polygon to finish one complete turn)] := b(n).
Lim_{n->infinity} b(n) = 1/2 (can be easily provenproved).
a(4) = 8 since it takes 3/8 of a full revolution of a square for a vertex to go from the highest point to the lowest point. When the vertex is at its highest position the square will be oriented at 45 degrees to the plane.
Denominator of time taken to fall by vertices for a vertex of a rolling regular polygons (Denominators)n-sided polygon to reach the ground.
Numbers that describe Denominator of time taken to fall by vertices of rolling regular polygons (Denominators).
proposed
editing
editing
proposed
Array[Denominator[(2 (# - 1) - Mod[#, 2])/(4 #)] &, 61, 3] (* Michael De Vlieger, Oct 06 2019 *)
proposed
editing