What secrets do squares reveal?

Is the universe constructed of numbers, and can mathematics uncover the nature of reality?

In this lesson, students learn about the Pythagoreans, who believed they could understand the universe by discovering its perfect, harmonious mathematical rules. Just as the Pythagoreans did thousands of years ago, students explore how to square numbers and find square roots, confront the weirdness of irrational numbers, and discover what happens when people’s most fundamental beliefs are thrown into doubt.

- Find areas of squares for whole-number and rational square widths
- Explore perfect squares of whole numbers and the finite differences between successive squares
- Find exact values of rational roots and an estimated value of √ 2 by testing and adjusting successive approximations
- Define irrational numbers, and learn that √ 2 is irrational
- Consider the nature of mathematical truth and how people respond when their mathematical beliefs are disproved

BBC, Pythagoras