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

Read More →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

Read More →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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Posted in ask uncle colin, geometry.

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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Posted in geometry.

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

Read More →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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Posted in geometry.

"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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Posted in geometry.

To-may-to / tomato; potato / po-tah-to; impossible exam / underprepared students. This time it's the hapless Kiwis who are making Downfall parody videos and complaining that their practice papers hadn't prepared them for stuff on the syllabus. Never mind; the formidable @solvemymaths has picked out the two most-complained-about questions, and

Read More →Before I begin: this post involves a puzzle and my attempt at a solution; everything above the horizontal rule is spoiler-free, but go beyond that at your peril. Some days, you can almost hear @colinthemathmo's chuckle as he innocently poses a question such as: Find all configurations of 4 points

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Posted in geometry.

On a recent1 episode of Wrong, But Useful, Dave mentioned something interesting2: if you take three regular shapes that meet neatly at a point - for example, three hexagons, or a square and two octagons - and make a cuboid whose edges are in the same ratio as the number

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