one-sided surface

In the first of a new series 'Imaging Maths', Plus takes an illustrated tour of an extraordinary geometric construction: the Klein bottle.

Maths in a minute

Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.

Arithmetic billiards

Need to find the least common multiple or greatest common divisor of two numbers? A billiard table of the right proportions holds the answers!
The maths of randomness

Randomness is surprisingly hard to define. Fortunately the mathematical language we use to describe it is beautifully well defined.
The real numbers and Cauchy sequences

We take the real numbers for granted, but what are they really?
Maths in a minute: The axioms of probability theory

Take a quick trip to the foundations of probability theory.
The two envelopes problem solved

Here's a resolution for one of probability theory's most famous paradoxes.