Browsing category geometry

A triangle puzzle

Like everyone else on Twitter, I’m a sucker for a nice-looking question, and @cshearer41 is a reliable source of such things. I particularly liked this one: There are two equilateral triangles inside this semicircle. What’s the area of the larger one? pic.twitter.com/Nvy01z2j5f — Catriona Shearer (@Cshearer41) November 7, 2018 Straight

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Sticks and Stones

Because I'm insufferably vain, I have a search running in my Twitter client for the words "The Maths Behind", in case someone mentions my book (which is, of course, available wherever good books are sold). On the minus side, it rarely is; on the plus side, the search occasionally throws

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A Christmas Decagon

Since it's Christmas (more or less), let's treat ourselves to a colourful @solvemymaths puzzle: Have a go, if you'd like to! Below the line will be spoilers. Consistency The first and most obvious thing to ask is, is Ed's claim reasonable? At a glance, yes, it makes sense: there's a

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Can you find a centre and angle of rotation without any construction?

Some time ago, I had a message from someone who - somewhat oddly - wanted to find a centre of rotation (with an unknown angle) without constructing any bisectors. (Obviously, if it was a right-angle rotation, they could use the set-square trick; if it was a half-turn, the centre of

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A Varignon Vector Masterclass

I recently listened to @mrhonner's episode of @myfavethm, in which he cited Varignon's Theorem as his favourite. What's Varignon's Theorem when it's at home? It states that, if you draw any quadrilateral, then connect the midpoints of adjacent sides, you get a parallelogram. Don't believe it? Try Mark's nifty geometry

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$\cos(72º)$, revisited again: De Moivre’s Theorem

In previous articles, I've looked at how to find $\cos(72º)$ using some nasty algebra and some comparatively nice geometry. In this one, inspired by @ImMisterAl, I try some nicer - although quite literally complex - geometry. De Moivre's Theorem I'm going to assume you're ok with complex numbers. If you're

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Ask Uncle Colin: A Troublesome Triangle

Dear Uncle Colin, I couldn't make head nor tail of this geometry problem: "If $a:b=12:7$, $c=3$, and $B\hat{A}C = 2 B\hat{C}A$, find the length of the sides $a$ and $b$." - Totally Rubbish In Geometry Hi, TRIG, and thank you for your message! (And don't put yourself down like that,

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Another @solvemymaths problem

Another geometry puzzle from @solvemymaths: I enjoyed this one -- no solution immediately jumped out at me, and I spend a great deal of time looking smugly at a way over-engineered circle theorems approach I can no longer remember. Let's label the apex of the triangle P, and the octagons

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A RITANGLE problem

When RITANGLE advises you to use technology to answer a question, you know it's going to get messy. So, with some trepidation, here goes: (As usual, everything below the line may contain spoilers.) It's easy enough to do this in Geogebra - but somehow a little bit unsatisfactory to move

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Daylight, Durlston Castle, and Where is Hamburg?

"Is Hamburg that much further north than London?" I furrowed my brow. Hamburg, to the best of my knowledge, is not that much further north than London. But here it was, written in stone (on the side of Durlston Castle in Swanage.) (I've transcribed the sign at the bottom of

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