I've come up with a way of demystifying e (2.718) for high schoolers. poshenloh.com/e I think it is much more intuitive than how e is currently taught, and could update all of the textbooks. Full article: arxiv.org/abs/2504.10664 In the USA, the first time people learn about e, it's usually taught as some irrational number 2.718, which is the limit of compound interest (1 + 1/n)^n, and then people do lots of exercise problems with the natural logarithm (ln) with confusion about why that is natural. Then in Calculus, many people just memorize that the derivative of e^x is e^x, without investigating a proof. I was guilty of that myself when I was in high school. I looked through 100 #math books representing 7 countries of curricula, and couldn't find a written reference with this approach. Now I'm crowdsourcing on social media. Does anyone know of a written reference with this visual method of teaching about e (2.718), which connects between (1 + 1/n)^n and the derivative of e^x being itself, in a way which is suitable for teaching Pre-Calculus students? The method is actually quite smooth, and laid out on the web link. Observe that all of the exponential functions y = a^x are really the same curve shape, just horizontal stretches of each other (like how ellipses are really all the same shape as each other, just stretched). So there's a unique number e for which e^x has its tangent line with slope 1 at x = 0. Use that to define e. It's well-defined due to the horizontal stretching argument, and that even immediately gives an easy way to numerically estimate e. The fact that the slope of the tangent line through (x, e^x) is just e^x also just drops out. [That observation has been made by many people before.] And to bridge this definition to the (1 + 1/n)^n limit, there's a visual argument using reflection and symmetry. I'm curious what people think.