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Figurate Numbers: Polygonal Number, Polite Number, Centered Square Number, Square Number, Triangular Number, Square Triangular Number : Polygonal Number, Polite Number, Centered Square Number, Square Number, Triangular Number, Square Triangular Number - LLC Books

Figurate Numbers: Polygonal Number, Polite Number, Centered Square Number, Square Number, Triangular Number, Square Triangular Number

Polygonal Number, Polite Number, Centered Square Number, Square Number, Triangular Number, Square Triangular Number

By: LLC Books (Created by)

Paperback | 1 May 2010

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Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Polygonal Number, Polite Number, Centered Square Number, Square Number, Triangular Number, Square Triangular Number, Figurate Number, Square Pyramidal Number, Centered Polygonal Number, Centered Hexagonal Number, Tetrahedral Number, Star Number, Pentagonal Number, Pronic Number, Hexagonal Number, Fermat Polygonal Number Theorem, Centered Triangular Number, Gnomon, Pentatope Number, Heptagonal Number, Centered Decagonal Number, Octahedral Number, Centered Heptagonal Number, Pentagonal Pyramidal Number, Octagonal Number, Centered Nonagonal Number, Centered Octagonal Number, Centered Pentagonal Number, Pollock Octahedral Numbers Conjecture, Dodecagonal Number, Decagonal Number, Nonagonal Number, Centered Cube Number, Hectagonal Number, Pyramidal Number, Heptagonal Pyramidal Number, Hexagonal Pyramidal Number, Myriagonal Number. Excerpt: A centered cube number is a centered figurate number that represents a cube . The centered cube number for n is given by n ] ( n + 1) . The first few centered cube numbers are 1, 9, 35, 91, 189, 341, 559, 855, 1241, 1729, 2331, 3059, 3925, 4941, 6119, 7471, 9009, 10745, 12691, 14859, 17261, 19909, 22815, 25991, 29449, 33201, 37259, 41635, 46341, 51389, 56791, 62559, 68705, 75241, 82179, 89531, 97309, 105525. (sequence A005898 in OEIS ) If C n is the n th centered cube number and P n is the n th square pyramidal number, then C n = P n + 4 P n 1 + P n 2. Centered cube numbers have applications in modelling the shells of atoms . See also (online edition) A hyperlinked version of this chapter is at A centered decagonal number is a centered figurate number that represents a decagon with a dot in the center and all other dots surrounding the center dot in successive decagonal layers. The centered decagonal number for n is given by the formula 5( n n )...