id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4476	Kobayashi, Yukio	A Pegagogical Study of Geometric Relations between the Sums of Cubic Integer Numbers and the Sums of Square Integer Numbers with the Sums of Odd Numbers	2022	14	.pdf	application/pdf	4513	210	76	The formula n∑ k=1 k3 = ( n∑ k=1 k )2 can be proved pictorially by expressing square numbers as sums of consecutive odd numbers, with slightly different diagrams from those of well-known pictorial proofs The relationship between the sum of square numbers and that of triangular numbers can pictorially be shown by expressing the square numbers as sums of consecutive odd numbers.	cache/ejpam-4476.pdf	txt/ejpam-4476.txt