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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)

Email: malkevitch@york.cuny.edu

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