Originally published at: https://boingboing.net/2019/02/19/learn-the-square-root-of-i-bo.html
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This is a wonderful and amazing thing and makes my inner math geek very happy.
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I was born as a defective unit. Maths are somehow more complicated for me than for some people. I always feel dumb, since my brother is way smarter than me, and he always teases me. And I think I’m pretty smart, don’t get me wrong, but numbers are out of my league.
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Bah. I seriously can’t add 1+1 in my head and get 2. Make a proof of it that is no problem (or was when I was studying it). Higher math has little to do with numbers.
I pull out my smart phone and use the calculator all the damn time. Math I can do, but arithmetic no fucking way.
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Is it me or does “beating the Euler out of it” sound… naughty?
Anyway, I couldn’t prove 1+1=2 if my life depended on it.
Mathematical demonstrations are my blind spot.
I managed non-linear partial differential equations and the math behind finite element methods and whatnot when I got my degree; it was work but it wasn’t a problem. But don’t ask me to prove anything.
I’m an engineer, just give me the tools and let me work with them.
I trust mathematicians.
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Is it (1+i) / sqrt(2)? Did I remember it right?
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yes Boundegar…and the other one…
Just halve the angle on the unit circle, and remember the 1, 1 over root 2, 1 over root 2 triangle… and remember there must be another solution 180 degrees away…
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The square root of Bob Ross is a kittie?
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Interesting material online on quaternions, and a surprising amount of drama about octonions, once you start looking.
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Agreed. Calculations are but a tiny part of the wonder that is Mathematics. The only reason that i can do arithmetic to the small extent that i can is because i’ve gotten so much practice having to do it while teaching higher math.
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This looks like a great channel . Thanks for showing it to us !
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Perhaps the next installment will explain how eπ i = -1
No, nothing can ever, ever explain (much less mathematically prove) this.
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That should actually be pretty clear from this video…
(bearing in mind that cos(π)=-1 and sin(π)=0)
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If you like questions like the one in the OP there are plenty of them answered on this channel
Although not in the same style.
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The best explanation I’ve seen for that related it to rotational angles in the complex plane. This might be the one:
https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/
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She looks like she loves her maths!
But it all looks really easy when someone else is doing the work.
This Hidden Brain episode: Close Enough: The Lure Of Living Through Others explores why watching videos of other people doing stuff is so attractive.
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Euler’s formula is a big gun to bring out for this little problem. Just write (a+bi)^2 = ±i, solve for a and b, and you’re there.
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Crap, here comes that unsettling feeling again…
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Obligs:
That was literally me while trying to help my kid with ‘common core.’
O_o
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