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Satanic science
There's no doubt that information is power, but could it be converted into physical energy you could heat a room with or run a machine on? In the 19th century James Clerk Maxwell invented a hypothetical being — a "demon" — that seemed to be able to do just that. The problem was that the little devil blatantly contravened the laws of physics. What is Maxwell's demon and how was it resolved?

From bridges to networks
How a cute 18th century puzzle laid the foundations for one of the most modern areas of maths: network theory.

What is cosmology?
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The Gömböc: The object that shouldn't exist
A Gömböc is a strange thing. It wriggles and rolls around with an apparent will of its own. Until quite recently, no-one knew whether Gömböcs even existed. Even now, Gábor Domokos, one of their discoverers, reckons that in some sense they barely exists at all.

Mysterious neutrinos
Research into the bizarre world of neutrinos helps to piece together the creation story of the Universe.

Sending flu packaging
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Most of us are familiar with the Cartesian coordinate system which assigns a pair of coordinates (x,y) to each point p in the plane: to get to p from the point (0,0) you walk a distance x along the x-axis and a distance y along the y-axis.

But there's another way of locating points on the plane, which is very nice too. You could assign to each point p the pair of numbers (r, φ), where r is the distance from p to (0,0) along a straight radial line, and φ is the angle formed by that radial line and the positive x-axis. These new coordinates are called polar coordinates. For example (measuring angles in degrees), the point with Cartesian coordinates (0,1) has polar coordinates (1,90) and the point with Cartesian coordinates (-2,0) has polar coordinates (2,180).

Polar equations give you a nice and easy way to describe shapes that are harder to describe in Cartesian coordinates. For example, a circle with radius 2 centred around (0,0) is given by the simple expression

r = 2,

since it captures all points at distance 2 from (0,0).

But our favourite is the equation

r = a sin(b φ).

It gives you a pretty rose petal where the number b (positive or negative) controls the number of petals: if b is odd then the rose will have b petals and if it's even then the rose will have 2b petals. The number a (positive or negative) determines how long the petals are.



It's amazing what you can do by changing coordinates!

See the Plus article How do we hallucinate? for an application of polar coordinates.