Re:Stacking Triangles for Fun and Profit
by gjm11 on Thursday April 11, 2024 @06:42PM
(#40007571)
Yup!
(If I were trying to present this stuff in a maximally-elegant order without too much regard for what order human brains like to learn things in, the order of things would be: complex numbers, calculus, trigonometry. Then we define something that we might initially call e(t) to satisfy the differential equation de/dt = ie, and observe that having e and e' at right angles means that |e| remains constant, which means that |e'| also remains constant, so if we start with e(0)=1 then we have a point moving at unit speed around the unit circle, etc. Keep the linkage between the geometrical and formal points of view there at all times. But I suspect this wouldn't be great paedagogically for the majority of students.)
(If I were trying to present this stuff in a maximally-elegant order without too much regard for what order human brains like to learn things in, the order of things would be: complex numbers, calculus, trigonometry. Then we define something that we might initially call e(t) to satisfy the differential equation de/dt = ie, and observe that having e and e' at right angles means that |e| remains constant, which means that |e'| also remains constant, so if we start with e(0)=1 then we have a point moving at unit speed around the unit circle, etc. Keep the linkage between the geometrical and formal points of view there at all times. But I suspect this wouldn't be great paedagogically for the majority of students.)