anyone remember this maths problem discussed here a year or two ago?(12 Posts)
I'm trying to remember where a maths problem came from that someone posted her a couple of years ago. I think it was from one of the maths competitions (probably intermediate), but although I've looked through them, I can't seem to see it.
It was a complex shape (hexagon/star like i think) made up of triangles of different colours. You were given an area of a small triangle and its base, I think. The question was about the area of a large triangle (or perhaps the area of the whole complex shape, which could be derived from the area of a large triangle).
It could be done with a brute force method of algebra and pythagoras, working out the height of one of the triangles and then using that in some way to find the overall sizes; it was complicated and ended up with fourth roots of things - but it did work.
And then there was the much more elegant way of solving it, which relied on the triangles being mathematically similar, probably equilateral (and you could tell the scale factor from the geometry of it), and then the area of the large one being proportional to the square of the scale factor.
It was a nice problem because it was possible - but very slow and needing quite a lot of determination! - to do it by the algebraic method, which perhaps seemed more obvious to students who are usually 'good' at maths, and yet so much nicer when you saw the other method. And I'd like to show someone again - but can't find it on the internet. I know it's there! I know we discussed it here and went over the various methods. But I just keep missing it when I look for it somehow. I could make up something similar, but it is never quite as good...
anyone remember it? Still have the link somewhere? thanks.
No sadly not, but thanks for trying. It was a mix of black and white (or grey) triangles in some sort of pattern.
Here's a link to all the recent ukmt challenges if you want to trawl through them
thanks; I had been going through them, and I kept thinking I'd spot it and recognise it, but either I've missed one (hard to keep track) or it wasn't from there - but I was so sure it was I thought someone else might recognise the description of the thread, as it was a busy one - but not sure if I can find enough key words to search for it on here (might have another go at that instead of the UKMT site, just for a change!). it was interesting as so many people at first assumed the slow, tedious, pythagorean/algebraic solution that got more and more complex, and found it harder to see what the easy solution was.
Did you post on the original thread? Or remember the username of anyone who did?
If it was in Chat, it would have been deleted.
That's the problem - I think it was chat, rather than here. Maybe I should repost my query there!
I tried my username but can't remember which one for sure I was using, and tried an advanced search of the right sort of words, but nothing so far. Was there someone like daddaddad or something who did maths? I think he was on it. But I have a feeling it was in chat and will be long gone.
There is also this. nrich.maths.org/11689. Perhaps I would just be quicker suggesting to have a look on nrich. they are always good for maths problems.
both those links take me to the same place?
But no, it's not that one, though thanks for looking. It was definitely about finding the area, and the elegant solution was to do it by using the square of the scale factor that you could work out from the info you'd been given, whereas the slow way was to use algebra and pythagoras to solve for the unknown heights etc and then work out the areas that way.
I'll have another look on nrich. It feels like a UKMT problem, and I'd have guessed intermediate (as I thought things like areas being proportional to squared scale factors was a sort of Yr9-11 topic, but maybe it's from an earlier one and I missed it on my quick glance).
I tried advanced search with the user names I remembered, like daddaddad, but nothing came up, so I'm guessing it was in Chat.
Sorry, I cut and pasted wrongly. The other was nrich.maths.org/6232, but by the sounds of it was wrong as well.
yeah ,not it either - though I did see that one on a UKMT paper as well, so nrich does have a lot of overlap.
I must be misremembering where it came from i guess. It doesn't sound like a typical 'homework' sort of problem, though, so must have been a competition of some sort, but searching the UKMT resource by topic didn't give me anything.
Oh well, i did find a few other interesting ones to use, though!
Just annoying I couldn't find that one, as it was nice, and very satisfying.
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