I’m 61, and I guess I first heard about e when I was 16. I got a degree in math since then. But I never quite got the purpose of e until now.
Bad texts and bad teachers are an extraordinary burden on math education.
[…] e. The “base of natural logarithms”, according to Wikipedia. Or, as the awesome Kalid at BetterExplained puts it, it is “the rate of growth associated with all continually gr… Yeah, there’s a mathematical constant talking about what those health drinks claim to do! […]
[…] If you want to know more about this intuitive approach to $e$ as 100% continuous growth, check this awesome article by Better Explained. […]
Brilliant! Thanks so much. I love the analogy of pi to e. I did electrical engineering in grad school and never really got an intuitive handle on e.
Thanks.
Great work Khalid! I am mathematics advisor in secondary education and I can say that I have never found such an original and creative contemplation of the number e. I’ll use some of your ideas in a future presentation with due reference to your name.
Please go on, you are an acute mathematical mind and you, so to say, make mathematics land from the heavens in a very tangible, intuitive way. By the way, I do not know your mastering of higher mathematics but it would thrill me to read your intuitive approach to general topology ideas.
Wow, thank you Stathis, I really appreciate the kind words. I’d love to keep going as long as I can, and something like Topology would be a fun topic to explore. My formal math knowledge isn’t that deep (beyond a regular engineering education) and I’d like to get into more theoretical topics down the line. Thanks for the note!
Back then…it was all rote learning we did.
Atleast,I wish we had teachers like you.
Thanks Anupam, glad you enjoyed it! Many of us had rote learning experiences, but we can always share what helped move beyond it :).
Thanks for taking your valuable time to enlighten the rest of us. 18 years of education and thousands in tuition couldn’t explain e better than you did.
I read somewhere that math is the language of the nature. I think I get that a little more after reading this article.
Kalid! how are you??
I need help! can I get your email? or rather, I want to know the different ways of approximating e, I know the Compound interest one… and the 1/n!.. I was wondering If your could help me with the continued fraction and showing how e is irrational and trascedental… 
well nice job kalid, but don’t you think that the right formula on the top should
be (1+return)^return,and not (1+return)^x.Just for correctsy,anyway nice explained
Hi leotrim, thanks for the note. I might be misunderstanding your comment, but if you have return=50% and have it for x=3 periods of time, you’d get (1 + 50%)^3 = (1.5)^3 = 3.375. You don’t want to do (1 + 50%)^50%! 
I would like to thank you so much for your wonderfull insights. realy I am speachless
Thanks Michael, glad you enjoyed it!
clear + intuitive. thank you!
Thanks Cody!
WOW! Thank you Kalid! This article was out of this world! AWESOME
Thanks Angel glad you enjoyed it!
Excellent Khalid, clear, precise and fussfree!! Can you care to explain how this e concept is applied in mortgage calculations? Amortization of a home loan?
Hi RK, thanks for the note. I have some more on e with regard to interest rates at http://betterexplained.com/articles/a-visual-guide-to-simple-compound-and-continuous-interest-rates/ but home loan / mortgage amortization would be a good one as well! The key idea is you figure out the net amount of principal + interest paid over the term, then divide by the number of months for a consistent monthly payment that mimics the total payout the compound growth would give.