The Nature of Length, Area, and Volume in Taxicab Geometry

TL;DR

This paper explores the fundamental concepts of length, area, and volume within taxicab geometry, extending understanding beyond straight-line distances to include curves and spatial measures.

Contribution

It provides a comprehensive analysis of how length, area, and volume are defined and understood in taxicab geometry, an area with limited prior research.

Findings

Defines length of curves in taxicab geometry

Analyzes area and volume measures in taxicab space

Establishes foundational principles for taxicab geometric measures

Abstract

While the concept of straight-line length is well understood in taxicab geometry, little research has been done into the length of curves or the nature of area and volume in this geometry. This paper sets forth a comprehensive view of the basic dimensional measures in taxicab geometry.