hexagonal number
التعريفات والمعاني
== English ==
=== Noun ===
hexagonal number (plural hexagonal numbers)
(mathematics) The number of dots in a figure made up of partially overlapping dotted regular hexagons (6k dots arranged into a regular hexagon) of perimeter 6k for k = 1 ... n which grow out of a common vertex (and two shared or partially shared sides); a.k.a. “cornered hexagonal number”;
H
n
+
1
=
6
Δ
n
−
n
2
+
1
{\displaystyle H_{n+1}=6\Delta _{n}-n^{2}+1}
where
Δ
n
{\displaystyle \Delta _{n}}
denotes the nth triangular number.
Hypernym: triangular number
Hyponym: even perfect number
(mathematics) The number of dots in a figure made up of regular dotted hexagons (of perimeter 6k for k = 1 ... n) arranged concentrically around an extra dot at their common center; a.k.a. “centered hexagonal number”;
H
n
+
1
=
1
+
6
Δ
n
{\displaystyle H_{n+1}=1+6\Delta _{n}}
.
==== Hypernyms ====
figurate number
==== Translations ====