“Euler’s identity” is a flashy way of stating that a half-turn rotation in the plane is equivalent to a reflection across the center of rotation. This is a fact which can be easily understood by young children.
The part that makes the expression flashy is that the rotation is written via its logarithm, which can be represented as the length of a circular arc (“angle measure”).
It’s a useful fact to know, but is vastly overrated.
The part that makes the expression flashy is that the rotation is written via its logarithm, which can be represented as the length of a circular arc (“angle measure”).
It’s a useful fact to know, but is vastly overrated.