myrmepropagandist on Nostr: Math people. Do you have an intuitive *geometric* reason why interlacing the power ...

Math people. Do you have an intuitive *geometric* reason why interlacing the power series of sin x and cos x gives the series for eˣ?

Do you have a way that you *visualize* growth whose rate is exactly its present value coming out of the unit circle as sine and cosine do?

I know the equations, and the proofs and they aren't convoluted and probably "enough" but I hope someone can share their mental images. Even if they aren't fully formed.