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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: 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.
Maths in a minute: Take it to the limit 
Sequences of numbers can have limits. For example, the sequence 1, 1/2, 1/3, 1/4, ... has the limit 0 and the sequence 0, 1/2, 2/3, 3/4, 4/5, ... has the limit 1. But not all number sequences behave so nicely. Can we still discern some sort of limiting behaviour?
Maths in a minute: Countable infinities 
An infinite set is called countable if you can count it. In
other words, it's called countable if you can put its members into
one-to-one correspondence with the natural numbers 1, 2, 3, ... .
Maths in a minute: Clever sums 
How would you go about adding up all the integers from 1 to 100? Tap them into a calculator? Write a little computer code? Or look up the general formula for summing integers?
Maths in a minute: Regression to the mean 
Sometimes you just can't argue with the evidence. If a large sample of very ill people got better after dancing naked at full moon, then surely the dance works. But hang on a second. Before you jump to conclusions, you need to rule out a statistical phenomenon called regression to the mean.
Maths in a minute: St Paul's dome
The dome of St Paul's, rising elegantly above London since the cathedral was rebuilt late in the seventeenth century, hides an intriguing early example of the interplay between maths and architecture.
Maths in a minute: The prisoner's dilemma 
Sometimes people are nasty when it would have been better to be nice.