The geometric interpretation of sin x = x - x³/3! + x⁵/5! -...

We first learnt sin x as a geometric object, so can we make geometric sense of the Taylor series of the sine function? For a long time, I thought it was just my dream, but actually, it is not! This proof only uses very elementary methods, and depending on your definition of calculus, doesn’t actually use calculus. The most we are using is a limiting process, and definitely no differentiation or integration here. This proof is very beautiful - not only that it unveils the geometric meaning of each term in the series very beautifully, but also understandable by a normal high-school student with a little bit of patience. I am very surprised that it has not appeared on YouTube before, and even if it does exist on the internet, it is far too unpopular, and so I have to bring this up! Obviously this is not my proof. See the sources below. Sources: (equations of the