Probability crops up in many places in physics, not least quantum mechanics and statistical mechanics, where we are only sure of things in an average or 'statistical' sense. Dealing with probabilities can be a headache for many students. They are also a headache for many in everyday life. There are numerous occasions where we need […]

Continue reading# Tag: maths

## The universal joint

…No, it isn’t something everyone smokes… But it is common in machine mechanisms. The universal joint is a neat way of turning rotation in one plane into rotation in another. A common use is on driveshafts where you want the direction of the shaft to bend. There’s a neat animation on Wikipedia of how the […]

Continue reading## The world’s most beautiful equation

Don't miss the BBC poll on what is the world's most beautiful equation. Are you a fan of Einstein's field equation, or does the Riemann zeta-function hold you in raptures? There's some great commentary on the twelve candidates here. How did I vote? Well, that would be telling, but the fact that my very first […]

Continue reading## Calculating pi with darts

I love this one. Really, it's maths not physics, but there is a bit of experimental physics creeping in at the fringes when the experimenters realize that the first method is biased. The second method is much better designed. Regrettably, pi-day (March 14th, 2015, or 3.14.15) only works if you use the US system of […]

Continue reading## How high is a winning cricket score?

I can't help thinking that the West Indies team got their run chase strategy wrong on Sunday night. They had a tricky task ahead of them. One might say the problem was one of their own making, judging from the rubbish that they served up to Guptill to hit at the end of tne New […]

Continue reading## The difference between a theoretical physicist and a mathematician is…

A mathematician can say what he likes… A physicist has to be at least partly sane J. Willard Gibbs What is it that makes a physicist sane (if only in part)? Everything has to be related back to the 'real world', or the 'real universe'. That is, a physicist has to talk about how things […]

Continue reading## When energy conservation doesn’t add up (or does it?)

In the last few weeks holes have been popping up all over Cambridge. They are being dug by 'ditch-witches' – pieces of machinery designed for making small-diameter tunnels for cabling – as part of the installation of fibre-optic cables for the much vaunted ultra-fast broadband. A ditch-witch is about the ultimate in machinery-obsessed-toddler heaven. We've […]

Continue reading## Saddle-points and today’s weather

I've been following the weather with interest this week. First of all, I was very glad when the wind and rain disappeared late last weekend. We were at a wedding in Whakatane on Saturday afternoon/evening, and boy, did it rain. With the wedding in a garden in something that was a bit more substantial than […]

Continue reading## Check those approximations

A common technique in physics is 'modelling'. This is about constructing a description of a physical phenomenon in terms of physical principles. Often these can be encapsulated with mathematical equations. For example, it's common to model the suspension system of a car as two masses connected by springs to a much larger mass. Here, the […]

Continue reading## Password entropy

As part of some 'NetSafe' training, I was shown this lovely xkcd cartoon http://xkcd.com/936/ . Password entropy. That's a good way of putting it. The statistical mechanics definition of entropy would be k ln W, where k is Boltzmann's constant, W is the number of permutations possible, and ln is 'the natural logarithm'. Higher […]

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