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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. From symmetry to Euclid's axioms, and from binary numbers to the prosecutor's fallacy, learn some maths without too much effort.
Maths in a minute: Counting numbers 
Are there more irrational numbers than rational numbers, or more rational numbers than irrational numbers? Well, there are infinitely many of both, so the question doesn't make sense. It turns out, however, that the set of rational numbers is infinite in a very different way from the set of irrational numbers.
Maths in a minute: The bridges of Königsberg 
How to make a hard problem easy by changing the way you look at it.
Maths in a minute: The Riemann sphere 
What happens when you shrink infinity to a point? You get a sphere!
Maths in a minute: Number mysteries 
Number theory is famous for problems that everyone can understand and that are easy to express, but that are fiendishly difficult to prove. Here are some of our favourites.
Maths in a minute: Not always 180 
Did you learn at school that the angles in a triangle always add up to 180 degrees? If yes then your teacher was wrong. Find out why here.
Maths in a minute: Arrow's theorem 
Is there a perfect voting system? In the 1950s the economist Kenneth Arrow asked himself this question and found that the answer is no, at least in the setting he imagined.
Maths in a minute: The missing pound 
Here's a well-known conundrum: suppose I need to buy a book from a shop that costs £7. I haven't got any money, so I borrow £5 from my brother and £5 from my sister. I buy the book and get £3 change. I give £1 back to each my brother and sister and I keep the remaining £1. I now owe each of them £4 and I have £1, giving £9 in total. But I borrowed £10. Where's the missing pound?
Maths in a minute: Newton's laws of motion 
We've been dabbling a lot in the mysterious world of quantum physics lately, so to get back down to Earth we thought we'd bring you reminder of good old classical physics.
Maths in a minute: Complex numbers 
How to take square roots of negative numbers and invent a whole new family of numbers in the process.