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You explained that 'a half turn rotation in a plane is equivalent to a reflection across the axis of rotation' to a child and they were able to figure out how '
by kittiepryde 7y ago
You explained that 'a half turn rotation in a plane is equivalent to a reflection across the axis of rotation' to a child and they were able to figure out how 'exp(i*pi)=-1' was derived? That's remarkable!
I think these children were on a much higher level than most adults that we'd still consider smart, I wouldn't put down anyone for not immediately seeing these two things as equivalent.
- jacobolus 7y agoNo, the children were able to understand how if you rotate a piece of paper by half a turn, all of the points end up the same distance from the axis of rotation, but the opposite direction from where they started. All of the stuff about exponential functions and angle measures and “imaginary” numbers just obfuscates the core idea.
- SilasX 7y agoBut the core idea involves why imaginary exponentiation means a rotation in the complex plane! If you don't have that part, you're not talking about i at all, you're just teaching the concept of rotation, with the same symbols as are used in complex math. You would have the exact same explanation if you were teaching about rotation unconnected to imaginary numbers or exponentiation at all!