Quick question. What mathematical constants would you say are worth memorising?
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@Nyoei I'm not sure there is much need to memorize any of them. More useful understanding how to apply them.
@freemo I suppose it's more of a 'Which ones should I learn to recognise on sight?' because I see a lot of wibbly symbols and I can never tell if they mean something profound or if they are just plugins.
@Nyoei The most commonly used ones you really need to know would be the following:
π (pi)
e (euler's number)
i (imaginary number)
and to a lesser extent φ (phi, golden ration)
Now if you want to include physics and not just pure math the list of essential constants is quite large.
As a side note while √2 is a very important number and worth exploring it isny usually represented as a constant in terms of notation. It is however called pathgoras' constant.
@freemo I love the Golden Ratio. I have whole books about it. Still haven't mastered it mind you... e i and pi have something to do with Eulers Identity but I haven't learned about that yet 😬
@Nyoei Well there is absolutely no advantage to memorizing digits other than practice i memorizing stuff. Just memorize a fractional approximation.
22/7 is off from pi by only ~1/791
If that isnt accurate eough then 355/113 approximates pi within ~1/3000000
Both of these are far more accurate than any digits you could memorize.
@freemo That is mind boggling. I hate fractions, but that is kind of beautiful. When it comes to working out stuff for engineering things I'd use a computer, but that has a rather lovely degree of precision there. I wish I was stronger with my maths. I have problems with things I can't understand at the root which makes learning incredibly hard for me.
I had a lot of parroting teaching at school with not much explanation as to why things were the way they were. It's not very helpful for people like me so I fell behind on the things I couldn't understand the rules for. I spent a lot of time in the library trying to work out why things were the way they were. Maths at least, once you get the rules in your head, is beautiful:)
I really pity my lecturers...
@Nyoei check out "continued fractions". They often make approximating numerical constants out as far as you want easy. Just need to memorize the pattern (if there s one) for a numerical constant.
@Nyoei Also i had the same experience with many teachers in my life sadly.
@freemo I am so sorry to hear that. Do you have similar problems to me? It makes for a beautiful mind but it also makes getting new info in there quite difficult unless you use a special hammer to force the facts in, different learning combinations, meds and a lot of naptime. Standard book learning is a non starter for me. My eyes glaze over and I am looking out of the window in seconds.
@Nyoei No not really the same problem. I learned from an early age to ignore teachers and to learn on my own and on my terms. If anything I'd say that taught me how to learn better than I might otherwise have.
@freemo I figured it wouldn't be. I am looking up the individual constants now. At least I memorised Pi to a reasonable level long time ago when I had a teacher who told me it would be fine to know it to 3sf. I disagreed violently with his assessment. I'd still like to understand more about it when I have the time. They should have maths philosophers in the world for people to talk to:D