Browsing category geometry

Some puzzles from Cav

A couple of puzzles that came my way via @srcav today: Cav’s solutions to this one are here; mine are below the line further down. Interesting angle puzzle — Cav (@srcav) July 8, 2019 And to this one, here Have a go yourself before you read on! I’ve

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A Tenth Of A Pizza

On Twitter, @Trianglemanscd posed a pertinent problem: Making pizzas tonight but cannot recall how to cut them in 10 slices. — Christopher Danielson (@Trianglemancsd) May 31, 2019 Stand back everyone! I have compasses and a straight-edge and I’m not afraid to use them; the Geogebra demonstration below shows one way

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Barney’s triangles

A puzzle from @Barney_MT: Find angle BDC This turns out to be a bit more demanding than I expected. There are spoilers below the line, showing a solution that took rather more time and space than the final polished version does. Spoilers below the line! Adding in circles When I’ve

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Barney’s Wedge

Once upon a MathsJam, Barney Maunder-Taylor showed up with a curious object, a wedge with a circular base. Why? Well, if you held a light above it, it cast a circular shadow. From one side, the shadow was an equilateral triangle; along the third axis, a rectangle. A lovely thing.

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Regions of a circle

On a recent MathsJam Shout, an Old Chestnut appeared (in this form, due to @jamestanton): If you’ve not seen it, stop reading here and have a play with it - it’s a classic puzzle for a reason. Below the line are spoilers. Counting is hard The first thing you’d probably

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Futility Closet, Fibonacci and Quadratic Residues

I love Futility Closet -- it's an incredible collection of interesting bits and pieces, but it has a special place in my heart because they love and appreciate maths. Not only that, they appreciate maths that I find interesting. The internet has many interesting miscellanies, and many excellent sites specialising

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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? — 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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