1, 2, 3 1,2,3, some inductive real sequences and a beautiful algebraic pattern
Abdymanapov S.A. Altynbek S. Begehr A. Begehr H.
1 November 2021De Gruyter Open Ltd
Analysis (Germany)
2021#41Issue 4245 - 256 pp.
By rewriting the relation 1 + 2 = 3 {1+2=3} as 1 2 + 2 2 = 3 2 {sqrt{1} {2}+sqrt{2} {2}=sqrt{3} {2}}, a right triangle is looked at. Some geometrical observations in connection with plane parqueting lead to an inductive sequence of right triangles with 1 2 + 2 2 = 3 2 {sqrt{1} {2}+sqrt{2} {2}=sqrt{3} {2}} as initial one converging to the segment [ 0, 1 ] {[0,1]} of the real line. The sequence of their hypotenuses forms a sequence of real numbers which initiates some beautiful algebraic patterns. They are determined through some recurrence relations which are proper for being evaluated with computer algebra.
convergence , plane parqueting , Sequence of real numbers
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Freie Universität Berlin, Institut für Mathematik, Arnimallee 3, Berlin, 14195, Germany
Kazakh University of Economics, Finance and International Trade, Zhubanov str. 7, Nur-Sultan, 010005, Kazakhstan
Fakultät für Informatik und Mathematik, Universität Passau, Innstraße 33, Passau, 94032, Germany
Freie Universität Berlin
Kazakh University of Economics
Fakultät für Informatik und Mathematik
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