Sitting in traffic in the middle of London gives you a lot of time to think. Here’s a fun problem born entirely of frustration sat waiting to cross the Hammersmith bridge.
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Let’s get pedagogical. Often when analysing a system, it is useful to break a component down into pieces, and figure out which are the important ones (if any). There are many techniques for this, here I’ll look at one called ‘singular value decomposition’ in the context of image compression.
Recently the extractor fan in my bathroom has started malfunctioning, occasionally grinding and stalling. The infuriating thing is that the grinding noise isn’t perfectly periodic – it is approximately so, but there are occasionally long gaps and the short gaps vary slightly. This lack of predictability makes the noise incredibly annoying, and hard to tune out. Before getting it fixed, I decided to investigate it a bit further.
A probability puzzle
I saw a ‘simple’ puzzle on the internet which I thought I’d have a crack at in an evening. Several furious scribblings on the bus and the sofa later, I finally have an answer. I’m so relieved I can’t help but share the joy.
This blog has been getting a bit too pop-science for my tastes recently. Card games? Word clouds? Urgh. Let’s do some proper physics. I hope you’re paying attention at the back.
When taking a picture of my new 55″ TV (humblebrag) I noticed a diffraction pattern of the reflection of the camera flash. Fortuitously, I had also recently bought a slightly too-powerful laser pointer from China which is the perfect tool to investigate such problems. Here’s a little write-up of my DIY measurements.
Vietnamese Maths Problem
A puzzle has been floating round the internet, apparently impossible and assigned to 8-year olds in Vietnam. How impossible is it? Here’s a quick look.
Fear of heights
I am a short man. I have an even shorter girlfriend. Odds are, any offspring would be short. Odds are, their partners would be similar or smaller in height, especially if they are male. Does this mean I am destined to be the heir to a slowly shrinking troglodyte race, my pristine DNA squirted from troll to troll until it degrades to a corrosive, fetid broth? Let’s put the thesaurus away and have a look.
How does a lens make an image?
I’ve talked before on this blog about the propagation of electromagnetic waves, and that’s not stopping any time soon. This time, I’d like to go through from first principles and demonstrate how a lens forms an image in all the gory details. Beware, there be maths ahead…
On which shaped planet am I the heaviest?
Continuing on from my last post concerning optimisation and Lagrange multipliers, I came across a neat little paper on the arXiv here, which asks and answers the question: what shape should a planet be to maximise the gravitational force at a given position? This is a fun problem, solved using an extension of the techniques from the last post, namely the use of Lagrange multipliers to optimise a function given some constraint.