Comments on: An Intuitive Guide To Exponential Functions & e http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/ Learning shouldn't hurt. Let's share the insights that made difficult ideas click. Tue, 16 Mar 2010 05:14:08 +0000 http://wordpress.org/?v=2.8.4 hourly 1 By: Kalid http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/#comment-275234 Kalid Sun, 14 Mar 2010 21:41:22 +0000 http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/#comment-275234 @AJ: Awesome, glad it helped! Yes, I think schools feel the need to use the "Calculus" version of e and miss out on its more humble origins. @Dimiter: You're welcome! Yep, I was in the same boat... at some point it struck me that I didn't really _understand_ this number we'd been using for so many years... @Anon: e has several equivalent definitions, just like a circle; I don't know if one is more official than the other. The integral/derivative is useful in many contexts, but unfortunately it implies you need to understand calculus to use e. An analogy: a circle can be defined as all points the same distance from a given point (the center), or x^2 + y^2 = r^2. Both convey the same idea, but one requires you to understand algebra. I've written more about this here: http://betterexplained.com/articles/developing-your-intuition-for-math/ @AJ: Awesome, glad it helped! Yes, I think schools feel the need to use the “Calculus” version of e and miss out on its more humble origins.

@Dimiter: You’re welcome! Yep, I was in the same boat… at some point it struck me that I didn’t really _understand_ this number we’d been using for so many years…

@Anon: e has several equivalent definitions, just like a circle; I don’t know if one is more official than the other.

The integral/derivative is useful in many contexts, but unfortunately it implies you need to understand calculus to use e.

An analogy: a circle can be defined as all points the same distance from a given point (the center), or x^2 + y^2 = r^2. Both convey the same idea, but one requires you to understand algebra.

I’ve written more about this here: http://betterexplained.com/articles/developing-your-intuition-for-math/

]]> By: Anonymous http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/#comment-275184 Anonymous Sun, 14 Mar 2010 04:08:56 +0000 http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/#comment-275184 Though most of this is correct, e is actually defined as the number that, when raised to the x power, is equal to both its derivative and its integral. Though most of this is correct, e is actually defined as the number that, when raised to the x power, is equal to both its derivative and its integral.

]]> By: Dimiter http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/#comment-274522 Dimiter Mon, 01 Mar 2010 15:36:34 +0000 http://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/#comment-274522 Thank you very much for explanation! I loved math when I was kid but after entering into Calculus and other maths I got scared because nobody explained me how we obtain those constants. We just had to learn them and not too look for a logic behind them. Many thanks again! Thank you very much for explanation!
I loved math when I was kid but after entering into Calculus and other maths I got scared because nobody explained me how we obtain those constants. We just had to learn them and not too look for a logic behind them.
Many thanks again!

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