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Problems and Solutions.

Authors :
Ullman, Daniel H.
Velleman, Daniel J.
Wagon, Stan
West, Douglas B.
Source :
American Mathematical Monthly. Aug2023, Vol. 130 Issue 7, p679-688. 10p.
Publication Year :
2023

Abstract

By the telescoping of the partial sums, the desired series converges to Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">lim</mi><msub><mrow><mi>T</mi></mrow><mi>n</mi></msub><mo>+</mo><mo> </mo><mrow><msub><mrow><mi>U</mi></mrow><mi>n</mi></msub></mrow></mrow></math> ht . Prove Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>P</mi><mi>A</mi><mo>=</mo><mi>P</mi><mi>B</mi></mrow></math> ht . Write Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi> </mi><mi>v</mi></mrow></math> ht for the sum of the entries of vector I v i . I Proposed by Colin Defant, Princeton University, Princeton, NJ, and Pakawut Jiradilok, Massachusetts Institute of Technology, Cambridge, MA. i Let Graph HT <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="script">P</mi><mo /><mo>=</mo><mo /><msub><mrow><mi>P</mi></mrow><mn>1</mn></msub><msub><mrow><mi>P</mi></mrow><mn>2</mn></msub><mo>...</mo><msub><mrow><mi>P</mi></mrow><mi>n</mi></msub></mrow></math> ht be a simple polygon that is a union of triangles chosen from the infinite plane tiling by equilateral triangles of side length 1. [Extracted from the article]

Details

Language :
English
ISSN :
00029890
Volume :
130
Issue :
7
Database :
Academic Search Index
Journal :
American Mathematical Monthly
Publication Type :
Academic Journal
Accession number :
169888602
Full Text :
https://doi.org/10.1080/00029890.2023.2210053