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Catriona Shearer
Maths teacher and fan of geometric puzzles.
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Catriona Shearer 20h
I probably won’t be bringing back this look.
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Catriona Shearer Mar 17
A unit circle sits in an equilateral triangle inside a square. What’s the total shaded area? This puzzle owes a lot to a picture by (and his students).
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Catriona Shearer Mar 16
Replying to @vanMathuysen @Ar_SH
So they do - sorry, I was misinterpreting your diagram. I honestly believed that case wasn’t possible but can’t now remember why. If I remember my reasoning I’ll let you know.
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Catriona Shearer Mar 16
Replying to @vanMathuysen @Ar_SH
Ah, but they won’t touch unless it touches at a vertex, right? Or in the centre.
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Catriona Shearer Mar 16
Replying to @mathsjem
Well, I really have you to thank - our conversation about Purley prompted me to get in touch with an ex-colleague I’ve not seen for 2 years, and we went together. It was a great evening 😄
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Catriona Shearer Mar 16
Replying to @PokeItAndSee
😂 You obviously make a good team!
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Catriona Shearer Mar 16
The area where these two quarter circles overlap is 16. What’s the total shaded area?
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Catriona Shearer Mar 16
Replying to @sanjaysingh13
Yes, it looks convincingly close, doesn’t it! The diagram’s actually drawn to scale (or as close as possible with felt tips!)
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Catriona Shearer Mar 16
Replying to @sanjaysingh13
Oh, I was going for the green one being the only right-angles triangle. But on reflection, I’m not sure I’ve ever worked out if the blue and red triangles are right-angled, I just assumed they weren’t!
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Catriona Shearer Mar 16
Replying to @vanMathuysen @Ar_SH
Oh, could you share your diagram? When I first wrote the puzzle I decided that the only way two equilateral triangles could touch like this was if the second either touched at the midpoint of a side, or at the bottom vertex of the first. I could well have missed a case.
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Catriona Shearer Mar 16
Replying to @sanjaysingh13
I’m not sure what you mean by an implicit perpendicular. But if it helps, I’m pretty sure only one of these triangles is right-angled.
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Catriona Shearer Mar 15
Oooh, I found some tiles just like this in our store cupboard this week! Can you share any tasks you were using them for?
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Catriona Shearer Mar 15
Replying to @Ar_SH @vanMathuysen
I think that can be implied from the information given. It took a while to convince myself - but if you try to actually draw it differently, you might see why it won’t work .
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Catriona Shearer Mar 15
Replying to @OHSMaths @chalkdustmag
Love it 😍
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Catriona Shearer Mar 15
I’m very excited about the issue 9 launch party later today - my third mathsy weekend in a row! To celebrate, here’s an old puzzle all about the number 9:
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Catriona Shearer Mar 14
Ooh yes, that was a fun problem. Can you remind me what the original question was?
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Catriona Shearer Mar 13
Replying to @helenarney
Happy to, although I think you need to follow me first.
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Catriona Shearer Mar 13
For change ringing, yes. [Ringers split into those who ring changes (tower bells and handbells) and those who ring tunes (handbells only). Tune ringers often use music though.]
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Catriona Shearer Mar 13
On the other hand, there are definitely some people who love this kind of challenge, especially something so mathematical!
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Catriona Shearer Mar 13
It's probably not impossible mechanically (I haven't checked carefully), but it would be really hard in other ways. Ringers usually learn a pattern and then perform from memory, so no one practises ringing from a visual aid. This would be very hard to memorise, though.
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