I’ll be the first to admit, this is a post I wrote mainly to scratch an itch of mine and so may have an audience of approximately 1. Fortunately in my previous life as a physicist I found that approximations can actually encompass many orders of magnitude, so perhaps we’re on to a winner here? Let’s find out.
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Forgive me for writing yet again about the weather, but
Of course it remains to be seen exactly how terrible, and in great and unrelenting detail. How better to honour the time-worn traditions of my people?
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Matt Parker, employing the enviably pithy prose typical of a content creator forged on the unforgiving fires of social media, asked the simple question back in 2018:
How thick is a three-sided coin?
Translated into mathematician-ese, this means
What aspect ratio of a flipped coin leads to the chance of landing on either edge being the same as landing on a particular face?
Such is Matt’s reach that this question has been answered thoroughly many – times – before, but that’s never discouraged us. Let’s take a look.
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Here’s a fun question – let’s consider, purely in the abstract, the notion of quickly putting on a lot of weight. If, hypothetically, one were to weigh themselves every day and, conceptually, throw away all of the results which showed an increase in weight, what, in a strictly Platonic sense, are the odds that actually they’re just a fat shit not actually losing any weight?
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It’s always exciting when a new 3Blue1Brown video emerges – Grant has an incredible sense for the intuitive visualisation of complex concepts (pun intended). His most recent on Newton fractals however really pushes the bar, and I couldn’t help but have a go at emulating it.
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Matlab is an archaic piece of software, is stupidly expensive, has a ridiculous syntax, horrible UI, and a whole host of bizarre quirks that you just put up with because that one grad student 10 years ago wrote a controller in it for a camera from a company which no longer exists and your supervisor refuses to buy a new one because apparently that’s a ridiculous price for only 14 bits of dynamic range.
Deep breath.
And despite all that, when I was in the zone I’m not sure I’ve ever been as effective in another piece of software. Let’s see about bringing it up to scratch.
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After my last post, where I noted that 45 degrees was the optimum angle to shoot a projectile the farthest, a commenter asked if the same was true for jumping from a swing. “Of course!” I initially thought. As we shall see, it isn’t actually that simple.
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I’ve got a house now which, amongst other things, means that all of my future posts will be depressingly domestic. In particular, as I sat watching a sprinkler water my new well-shaded lawn, I noticed that some parts of grass were being watered more than others. It wouldn’t be right to fix these kinds of problems without first wringing all possible interest from them however, so let’s first understand what’s going on from the safe, dry comfort of a computer screen.
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Since the start of lockdown, I’ve found ever more reasons to be grateful for the surprisingly sunny postage-stamp of a garden I enjoy here in London. I am however moving to a new house soon, and have been curious to know how the new garden will fare in comparison. Hopefully so are you, as we’re about to enjoy it in painful detail.
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One of the many sad consequences of the current lockdown, possibly the most unfortunate of all, is that the famous Cooper’s Hill Cheese-Rolling competition will almost certainly not be taking place this year. In the spirit of finding light in the darkness, let’s at least have a look at how we may improve it for next year. With maths!
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Almost looks like work 