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ERIC Number: EJ886050
Record Type: Journal
Publication Date: 2010-May
Pages: 8
Abstractor: As Provided
Reference Count: 0
ISBN: N/A
ISSN: ISSN-0746-8342
Using Squares to Sum Squares
DeTemple, Duane
College Mathematics Journal, v41 n3 p214-221 May 2010
Purely combinatorial proofs are given for the sum of squares formula, 1[superscript 2] + 2[superscript 2] + ... + n[superscript 2] = n(n + 1) (2n + 1) / 6, and the sum of sums of squares formula, 1[superscript 2] + (1[superscript 2] + 2[superscript 2]) + ... + (1[superscript 2] + 2[superscript 2] + ... + n[superscript 2]) = n(n + 1)[superscript 2] (n + 2) / 12. More precisely, the following algebraic equivalents are derived, [image omitted]. The proofs obtained literally count squares, namely lattice squares whose vertices are in an "n" x "n" grid. For the first formula, only lattice squares aligned to the grid are counted; for the second formula, aligned "and" tilted squares are counted.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A