Revision as of 05:33, 14 June 2024 edit 2601:646:8080:1ebe:8ee7:6a56:1ca3:2e08 (talk) →Explicit formulas: Typo Tags: Mobile edit Mobile web edit ← Previous edit		Revision as of 15:11, 11 November 2024 edit undo Dyspophyr (talk \| contribs) 427 edits →Other characterizations: link -> simple continued fraction Next edit →
Line 71: ==Other characterizations== All square triangular numbers have the form <math>b^2c^2</math>, where <math>\tfrac{b}{c}</math> is a [[Convergent (continued fraction)\|convergent]] to the [[simple continued fraction\|continued fraction expansion]] of <math>\sqrt2</math>, the [[square root of 2]].<ref name=Ball> {{cite book \| last1 = Ball \| first1 = W. W. Rouse \|author-link1 = W. W. Rouse Ball \| last2 = Coxeter \| first2 = H. S. M. \|author-link2 = Harold Scott MacDonald Coxeter \| title = Mathematical Recreations and Essays \| url = https://archive.org/details/mathematicalrecr00coxe \| url-access = limited \| publisher = Dover Publications \| ___location = New York \| year = 1987 \| page = [https://archive.org/details/mathematicalrecr00coxe/page/n72 59]\| isbn = 978-0-486-25357-2 }} </ref>

Square triangular number: Difference between revisions