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 ...

The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory. The rational numbers are the most familiar numbers: 1, -5, ½, and every ...

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 ...

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 ...

A rational number can be written exactly in the form \(\frac{a}{b}\), where 𝑎 and 𝑏 are integers, while an irrational number cannot.

In the early 1970s mathematician Donald Knuth spent a sabbatical with his wife in Norway. The time was meant to be spent relaxing. Yet one night he woke up his partner in a state of agitation. He ...

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 — ...