Tag: maths
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£4,803.40 a Year for Water?
When we moved house, Thames Water failed to set us up an account correctly, and the hacky workaround they came up with claims that we spent our first 11 hours in the Chicory House perhaps pouring three tonnes of water into an ankle-depth 5×10 metre swimming pool.
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FlipFlop Solitaire's Deck-Generation Secret
I enjoy a mobile game called FlipFlop Solitaire, which provides a few thousand pre-seeded decks that are guaranteed "winnable". This blew my mind for a little while - how can you be sure that these shuffles are all winnable? But then I worked out a way to achieve exactly that result... by thinking in reverse!
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Visualising Forged In The Dark probabilities
Blades in the Dark (and other Forged In The Dark-based games) use a highest-value-from-D6-dice-pool mechanic to resolve actions. I was looking for a visualisation of the resulting probabilities, but couldn't find one... so I made my own.
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How I Learned the Pythagorean Theorem
I clearly remember the day I first learned the Pythagorean theorem, because I had a problem I wanted to solve and a practical application that I wanted to use it on. Let's re-create the experience, and see if I can take any lessons about how to support my kids in their own mathematical journeys.
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I'm looking at a listing for a ¼" to ⅝" screw adapter, for which the seller warns that I should "please allow 1-3cm error".
A 3cm error would mean that a ⅝" screw could result in a screw thread anywhere between 1⅘" and... minus half an inch, I guess? (I don't even know how to make the concept of negative lengths fit into my brain.)
I suppose this seller could send me an empty envelope and declare that it contained an infinitesimally small adapter. At which point... I'd be the one that was screwed!
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Highlighted item description from an eBay listing. The highlighted section shows that the listing is for a quarter inch to a five-eighth of an inch adapter made of a premium aluminium alloy, and that the buyer should "please allow 1-3cm error due to manual measurement".
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Sometimes people connect my unusual name to popular culture. They say things like "Oh, Q like James Bond?" or "Oh, Q like Star Trek?".
I think their choice of franchise tells me more about them than they learn from my answer, which is usually "No, Q like the set of rational numbers."
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Do you know the story of how Tom Lehrer hid an Easter Egg in an academic paper he wrote at the NSA, and his joke wasn't discovered for almost six decades?
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Build Colors from Colors with CSS Relative Color Syntax
Caleb Hearth wrote an inspiring piece about CSS's new OKLCH functions, and now I want nothing more than to (re-?)implement something using this colour model!
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Hero of Alexandria
Hero of Alexandria is my hero. And it's not for the steam engine he didn't invent (that was Vetruvius), nor for his formula for the area of a triangle, nor even for his programmable robot (yes, really). It's for his square root algorithm.
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D20 with Advantage
D&D players spend a lot of time rolling D20s. Sometimes they 'roll with advantage' - that is, roll two dice and take the largest. Last night I dreamed I derived the probability matrix for such rolls, and it got me thinking... could you construct a single die that rolls 'D20 with Advantage'?
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Sisyphus: The Board Game (Digital Edition)
I implemented a terrible digital version of a truly stupid board game idea. My excuse is illness, I guess?
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Mathematics of Mid-Journey Refuelling
Dan uses the Secretary Problem to work out which filling station to pull over at for the cheapest fuel on a long journey.
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Here’s What a Googol-to-One Gear Ratio Looks Like
Jason Kottke reports that Daniel Bruin has built a machine that demonstrates a truly absurd gear ratio, and Dan does some silly back-of-napkin maths.
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Who finished second?
Nick Berry shares an amazing maths/logic puzzle, and Dan encourages you to give it a go for yourself.
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This equation will change how you see the world
Veritasium's latest video looks at the patterns of order and chaos in fractals, and Dan thinks it's surprisingly good.