Browsing category geometry

Ask Uncle Colin: Shouldn’t this be simple?

Dear Uncle Colin, I've got a funny square and I can't find $x$. Can you help? - Oughta Be Simple, Can't Unravel Resulting Equations Hi, OBSCURE, and thanks for your message! You're right, it ought to be simple... but it turns out not to be. It is simple enough to

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My Stab At Colin’s Puzzle

The estimable @colinthemathmo suggests a method for estimating the radius of the earth, which he credits to a sundial expert friend named Mike: Stand on a wall, perhaps two metres high, and wait for sunrise. When you see the sun just peak above the horizon, start the stopwatch, and jump

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The Return Of The Cav

It's good to see @srcav back in the twitter and blogging fold - he's been missed! As part of his comeback, he shared this lovely geometry puzzle: Assuming the situation is symmetrical (which it needs to be to get a sensible solution), there are - as usual - several ways

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Ask Uncle Colin: Trouble in Sector ABC

Dear Uncle Colin, I got stuck on this sector question, which asks for the radius of circle $P$, which touches sector $ABC$ as shown. I'm given that $ABC$ is a sector of a circle with centre $A$ with radius 12cm, and that angle $BAC$ is $\frac{\pi}{3}$. My answer was 3.8cm,

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Ask Uncle Colin: how big do the patches on a football need to be?

Dear Uncle Colin, I'm trying to sew a traditional football in the form of a truncated icosahedron. If I want a radius of 15cm, how big do the polygons need to be? -- Plugging In Euler Characteristic's Excessive Hello, PIECE, and thank you for your message! Getting an exact answer

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Another of Alison’s Ace Puzzles, Revisited

This is a guest post from @ImMisterAl, who prefers to remain anonymous in real life. It refers to the problem in this post: a semi-circle is inscribed in a 3-4-5 triangle as shown; find $X$. As with any mathematical problem, my first thought was to sort out exactly what I

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A surprising overlap

Every so often, my muggle side and mathematical side conflict, and this clip from @marksettle shows one of them. My toddler's train track is freaking me out right now. What is going on here?! pic.twitter.com/9o8bVWF5KO — marc blank-settle (@MarcSettle) April 6, 2016 My muggle side says "wait, what, how can

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Another of Alison’s Ace Puzzles

A nice puzzle this week, via NRICH's magnificent @ajk44: a semicircle is inscribed in a 3-4-5 triangle as shown. Find $X$. I think it's a nice puzzle because Alison's way of doing it was entirely different to mine, but thankfully got the same answer. You might like to try it

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Ask Uncle Colin: Bridges, Donkeys and Triangles

Dear Uncle Colin, I'm struggling to understand why, if you know a triangle has two sides the same, the base angles must be the same. Can you explain? -- I'm Struggling Over Some Coherent Explanation Leveraging Equal Sides Hi, ISOSCELES, and thanks for your message! There are several good proofs

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Going around incircles

"Did you know," asked a student at third-hand1, "that the in-circle of a 3-4-5 triangle has a radius of 1?" That's the kind of thing I'd normally just fire up GeoGebra to check, but I was in the middle of a podcast! The best I could do was check to

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