An Arithmetic Triangle Arising From a One-Way Street Grid. (15th March 2023)

• Record Type: Journal Article
• Authors: Richmond, Tom; Sword, Mia
• Is Part Of: College mathematics journal. Volume 54:Number 2(2023)
• Page Start: 113
• Page End: 122
• Publication Date: 2023-03-15
• Subjects: 05A10 -- 11B65; Mathematics -- Study and teaching -- Periodicals; Mathematics -- Periodicals; Mathematics; Mathematics -- Study and teaching; Periodicals; 510.071
• DOI: 10.1080/07468342.2023.2186083
• Languages: English
• ISSNs: 0746-8342

Abstract

Summary: Pascal's triangle arises by counting the number of shortest paths from (0, 0) to ( n, k ) on a square street grid. The length of the shortest path is the Manhattan distance from (0, 0) to ( n, k ). We consider the case of a square street grid of one-way streets, with successive parallel streets being oppositely directed. We investigate the associated distance function q (which is only a quasi-metric, since q ( A, B ) may differ from q ( B, A )) and the arithmetic triangle obtained by counting shortest routes on the one-way grid from (0, 0) to ( n, k ).