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Diagonals: Part I

Posted February 2004.
Feature Column Archive

1. Introduction

Who has not been in a hurry or tired and been tempted to "cut across the diagonal" to save time or effort even if doing so would make a mockery of attempts to make the lawn look nice?

Diagram showing how to save time by cutting across the diagonal of a rectangle

Using the Pythagorean Theorem you can compute how much distance you save.

The unifying theme of this column is the value of thinking about and using diagonals: a window for lots of fascinating mathematics. Knowing the value of a tool in one situation often allows one to put ideas to work in unexpected ways to create interesting new mathematics elsewhere.

Joseph Malkevitch
York College (CUNY)


  1. Introduction
  2. What is a diagonal?
  3. Triangulations and ears
  4. Art gallery theorems
  5. Where do new problems come from?
  6. References