4 ms·
My vote as an amateur mathematician would be “rotational” numbers. Everything having to do with complex numbers secretly (or not so secretly) has to do with ang
by zwkrt 5y ago
My vote as an amateur mathematician would be “rotational” numbers. Everything having to do with complex numbers secretly (or not so secretly) has to do with angles and rotations, and it would be easy to describe to a class of middle schoolers that if you want to do math to describe how things rotate, it makes sense that you need a 2D space.
- abecedarius 5y agoTwirly numbers, to me.
- deleted 5y ago[deleted]
- hammock 5y agoThis just made it click for me why imaginary numbers are used in electrical engineering
- jacobolus 5y agoTristan Needham’s word is “amplitwist”, meaning a scaling composed with a planar rotation. A complex number should be thought of as the quotient of plane vectors: a quantity z = v/u which when multiplied by vector u yields v: that is zu = v. (Important note: multiplication of a complex number by a vector is not commutative, zu ≠ uz.) For more: http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf
- fsloth 5y agoWell, IMO their rotational feature is kind of the accidental, happy and mysterious side-effect that starts from the "simple" computational trick of defining sqrt(-1) being i, and taking the calcuslations from there. I would philosophically say "Completeness" is a more important property (since now negative roots have a meaning attached to them). But their rotational aspect is perhaps more mind blowing.
- zwkrt 5y agoI disagree but I don’t have an incredibly concrete argument, only an intuition that in the case of complex numbers, our mathematical formalism for solving equations proceeded our mathematical intuition about cyclical processes.