Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

Irrational numbers are numbers that cannot be expressed as the ratio of two whole numbers. This is opposed to rational numbers, like 2, 7, one-fifth and -13/9, which can be, and are, expressed as the ...

Originally defined as the ratio between the circumference of a circle and its diameter, pi — written as the Greek letter π — appears throughout mathematics, including in areas that are completely ...

The ancient scholar Hippasus of Metapontum was punished with death for his discovery of irrational numbers—or at least that’s the legend. What actually happened in the fifth century B.C.E. is far from ...

When my students grow too dependent on their calculators, I ask them to find a number that, when multiplied by itself, gives them 2. Students quickly see that since 1² = 1 and 2² = 4, the answer has ...

This article is adapted from Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else by Jordan Ellenberg. © Penguin Press 2021 ...

When you purchase through links on our site, we may earn an affiliate commission. Here’s how it works. Originally defined as the ratio between the circumference of a circle and its diameter, pi — ...