I am grateful to my friend and former Swansea colleague Dr Farzin Deravi of University of Kent at Canterbury who read my blog post on Euler’s identity (“The Most Beautiful Equation in the World”) via Facebook and told me about this video proof of the equation:
It’s well put together, but for me crucially omits the vital step that substitutes cos ? = -1 and sin ? = 0 to reduce ei? = cos ? – i sin ? to ei? = –1 + 0 which of course can be rearranged to give ei? + 1 = 0.
This was not the only “Euler Video” available on YouTube, looking further, I found this nice example, also a proof of Euler’s identity, that shows what you can do with a tablet and screen recording software.
Two very inspirational demonstrations of the power of video in the teaching of mathematical concepts.