this post was submitted on 11 Jan 2024
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Multiplying with q negative does genuinely correspond to a 180° rotation around the origin in the complex plane (plus a scalar multiplication of course)
Very intuitive to kids
I take your point, but honestly I'd bet many would be ready to learn about complex numbers a lot earlier if they were taught in this way.
Having such a memorable physical analogy "because I said so" is already miles better than the purely abstract "multiplying negatives makes a positive because I said so", even if it still doesn't mean you could teach extremely high level maths to six year olds.
Agreed. I'm trying to keep the reigns on an 11 year old, and we frequently talk both in what I would say is abstract. Also have to keep it somewhat grounded, because skipping multiple grades in math does not mean you will understand some things. Absolute value was an interesting conversation, and to be fair so was multiplying negatives.
I was already trying to visualize multiplying as a circle in my head and something clicks but cant grasp it.
Now reading that apparently There is a real mathematical link i am dying to learn more. Do you know of an online visualizer/simulation that helps showing what you just said?
Honestly, the best online resource I know of are the 3blue1brown videos on complex numbers
Any tool risks confusing you more, since multiplying in the complex plane can act quite unexpectedly when you move outside the real line for both parameters
Had a look around and this will quickly become one of my favorite media channels! Thanks!
https://www.3blue1brown.com/lessons/eulers-formula-via-group-theory
Minute 12 in the video is the most relevant, but the whole lesson is worth going through.
3blue 1brown is a great channel for challenging how you think about math in a beautifully animated fashion.
I just had a look on their channel. I think my old classmates would cringe if they knew how excited i got seeing these thumbnails and titles.
All my initial scientific inspiration have gotten sucked dry in the meat mill that is the education system, but living in the age of educational internet videos is big healer.
I got vertasium and steve mould. Kurtzegesagt is mandatory for everyone by now i hope, i still follow Vsauce but i miss Michael. Got any other recommendations?
Mathloger, numberphile, computerphile, Sixty symbols: more good math/computer science theory channels
applied science, breaking taps: truly amazing "garage" engineering. They take on projects that you would normally expect to take a specialized lab.
alpha phoenix: his expertise is in materials science but he does delve a bit into electromagnetic questions
Mr P Solver: solving interesting problems computationally in pthyon
Eevblog: good electrical engineering insights with a nice Australian accent
Practical engineering: all the civil engineering questions you never knew you had
Stuff made here: what happens if a robotics expert has a generous fun projects budget and never sleeps
Tropical tidbits: discussion of the meteorology of tropical storms and hurricanes as they happen with none of the weather reporting sensationalism
I'm sure I'm missing some, but that should be a big enough list to add many hours to your watch list.
I have a physics degree, and 3 blue 1 brown's latest videos on light are amazingly presented in comparison to the vast majority of lectures I've sat through. It makes me hopeful that online video sharing can help improve pedagogy and not just be clickbait nonsense.
Maybe this help https://www.nagwa.com/en/explainers/280109891548/
Or you can search Argand Diagram