I've been reading the first few pages of and Mathematics Magazine in Vietnamese. The topic mentioned in the article is Radon transform. The idea is to use the technique to create the image from the scattering data associated to cross-sectional scans of an object. Basically, it has a wide application including CAT (medical scan), GPS (lonosphere) and searching for bombs, etc.
However, the most fascinating idea I found in this article was not the Radon transform since I don't understand yet how they deduced the formula. What really captured my attention was the idea of solving problems by posing predictions or conjectures. The beautiful thing is those predictions need not be true, they only need to be make sense in the context. After that, the data is collected and compare to eliminate the impossibles. By then, the solution would be arrived at.
It's probably not the most extraordinary concept. However, I always underestimated the applicable ability of this technique in solving mathematics problems. Anyone who reads a lot of Detective Conan would recognise this technique right away (there are 3 possible suspects but only one of them is the real culprit). On the other hand, solving maths to me is a bit linear. If I was given a problem, I would not predict the answer beforehand but attempting to solve it using the techniques I know right away. Thus, sometimes the technique does not apply and I meet myself in the dead end (the one with a big mirror that reflect myself back to me, telling me that I'm sucked this and that - I'll write more about this later).
I guess from now on, it would be an exercise for me then, to predict and estimate the scope of the solution before attempting to solve anything. Hopefully this would help to increase my productivity by reducing some thinking as well as calculations.
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