On Sunday I spent a great deal of time thinking about a question. A question presented in the Open Day I talked about yesterday that was used in Interviews for the 2019 Applicants. And it just kept whizzing around my head. I was watching TV with Mummy and Kunnu when I had to grab my notepad and have a go at it again. I annoyingly missed a big chunk of the show but it's okay because I now have two solutions to it!
This is a screenshot of the question. The diagram isn't perfect but that's not really the problem here. The question is: you are given the curve
y = x2 and you have three points: A, B and C, where B is the origin (0, 0). Find A and C such that the triangle is equilateral.
Although it took me a while (due to a idiotic mistake) my two methods are (1) using the length of the sides and (2) using trigonometry
Solution for (1)
Solution for (2)
Now this is where it gets interesting. Dr Munro then suggested that from here he would ask students if this triangle could be similar to a 3, 4, 5 triangle (obviously no, due to the proportions being completely different). Then he wants us to MAKE IT INTO ONE!
I haven't got around to it yet because I have been annoyingly busy today (which, of course, means I was yet again unsuccessful at planning my time) but I definitely have some ideas. I'm going to have a go at it and update ASAP.
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