Intuitive Understanding of the constant “ee”

Potentially related-questions, shown before posting, didn’t have anything like this, so I apologize in advance if this is a duplicate.


I know there are many ways of calculating (or should I say “ending up at”) the constant e. How would you explain e concisely?

It’s a rather beautiful number, but when friends have asked me “what is e?” I’m usually at a loss for words — I always figured the math explains it, but I would really like to know how others conceptualize it, especially in common-language (say, “English”).


related but not the same: Could you explain why ddxex=ex “intuitively”?

Answer

If someone asks me, “what is e?” I sketch the graph of y=1/x, draw a line segment from (1,1) on the curve down to (1,0) on the x-axis, and ask, how far to the right do I have to draw another vertical segment to rope off an area of 1? Anyone who is familiar with the idea of graphing a function can appreciate that definition, and it’s not surprising that something with such a down-to-earth definition is going to turn up in lots of other places in Mathematics. And anyone who knows Calculus can be shown that all the other properties of e and of ex and of logx can be derived from this one property of e.

The yellow area equals the red one:

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Attribution
Source : Link , Question Author : sova , Answer Author : Gerry Myerson

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