formulasearchengine - User contributions [en]

Sloped armour

2013-06-12T08:36:43Z

122.160.24.75: /* The cosine rule */

In [[computer science]], a '''2–3 heap''' is a [[data structure]], a variation on the [[heap (data structure)|heap]], designed by [[Tadao Takaoka]] in 1999. The structure is similar to the [[Fibonacci heap]], and borrows from the [[2–3 tree]].

Time costs for some common heap operations are:

* ''Delete-min'' takes <math>O(log(n))</math> [[amortized time]].
* ''Decrease-key'' takes constant amortized time.
* ''Insertion'' takes constant amortized time.

== References ==

* Tadao Takaoka. [http://www.cosc.canterbury.ac.nz/~tad/2-3heaps.pdf ''Theory of 2–3 Heaps''], Cocoon (1999).

{{DEFAULTSORT:2-3 heap}}
[[Category:Heaps (data structures)]]

{{datastructure-stub}}

Lerner index

2013-05-27T04:45:20Z

122.160.234.74:

{{refimprove|date=August 2012}}
A '''dodecagonal number''' is a [[figurate number]] that represents a [[dodecagon]]. The dodecagonal number for ''n'' is given by the formula 5''n''2 - 4''n'', with ''n'' > 0. The first few dodecagonal numbers are:

:[[1 (number)|1]], [[12 (number)|12]], [[33 (number)|33]], [[64 (number)|64]], [[105 (number)|105]], [[156 (number)|156]], 217, 288, 369, 460, 561, 672, 793, 924, 1065, 1216, 1377, 1548, [[1729 (number)|1729]], 1920, 2121, 2332, 2553, 2784, 3025, 3276, 3537, 3808, 4089, 4380, 4681, 4992, 5313, 5644, 5985, 6336, 6697, 7068, 7449, 7840, 8241, 8652, 9073, 9504, 9945 ... {{OEIS|id=A051624}}

The dodecagonal number for ''n'' can also be calculated by adding the square of ''n'' to four times the (''n'' - 1)th [[pronic number]], or to put it algebraically, <math>D_n = n^2 + 4(n^2 - n)</math>.

Dodecagonal numbers consistently alternate [[Parity (mathematics)|parity]], and in base 10, their units place digits follow the pattern 1, 2, 3, 4, 5, 6, 7, 8, 9, 0.

By the [[Fermat polygonal number theorem]], every number is the sum of at most 12 dodecagonal numbers.

==See also==
* [[Polygonal number]]
* [[Figurate number]]
* [[Dodecagon]]

{{Classes of natural numbers}}
{{num-stub}}

[[Category:Figurate numbers]]

Capital adequacy ratio

2012-08-22T08:25:49Z

122.160.52.166: /* Use */

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2012-07-27T10:22:29Z

122.160.214.186:

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2012-03-09T05:55:04Z

122.160.132.94:

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