Plus.Maths.org
List by Author: Marianne Freiberger
Information is sophistication 
Kolmogorov complexity gives a high value to strings of symbols that are essentially random. But isn't randomness essentially meaningless? Should a measure of information assign a low value to it? The concept of sophistication addresses this question.
Information is surprise 
If I tell you something you already know, then that's not very informative. So perhaps information should be measured in terms of unexpectedness, or surprise?
Information is complexity 
There are many ways of saying the same thing — you can use many words, or few. Perhaps information should be measured in terms of the shortest way of expressing it? In the 1960s this idea led to a measure of information called Kolmogorov complexity.
Information is noisy 
When you transmit information long-distance there is always a chance that some of it gets mangled and arrives at the other end corrupted. Luckily, there are clever ways of encoding information which ensure a tiny error rate, even when your communication channel is prone to errors.
Information is bits 
Computers represent information using bits — that's 0s and 1s. It turns out that Claude Shannon's entropy, a measure of information invented long before computers became mainstream, measures the minimal number of bits you need to encode a piece of information.
Two-faced conic sections 
Play with our applets to explore the conic sections and their different definitions.
Introducing the Klein bottle 
A Klein bottle can't hold any liquid because it doesn't have an inside. How do you construct this strange thing and why would you want to?
The Sun, the Moon and trigonometry 
A little trig helps to find the relative distance to the Sun and Moon.
The limits of information 
Why there is a limit to how much better computer chips can get and what it's got to do with black holes.
Stubborn equations and the study of symmetry 
An impossible equation, two tragic heroes and the mathematical study of symmetry.