Why Does e Appear in Nature So Often?

  • Thread starter Thread starter quasar987
  • Start date Start date
  • Tags Tags
    Nature
AI Thread Summary
Exponential equations in physics often stem from the relationship a^[f(x)] = a^[f(x)] * lna * df/dx, though some textbooks lack a proof for this. The number e is questioned for its significance and why it frequently appears in nature, with many definitions being perceived as unintuitive. A key point discussed is that the integral from 1 to e of 1/x equals 1, highlighting a fundamental property of e. This relationship suggests a deeper mathematical significance that merits further exploration. Understanding why e is prevalent in various contexts remains a topic of interest among learners.
quasar987
Science Advisor
Homework Helper
Gold Member
Messages
4,796
Reaction score
32
oops there's an extra m in my topic title, I was going for why e. :wink:

I believe most the the exponential equations in physics come from the fact that a^[f(x)] = a^[f(x)] * lna * df/dx but the book I had in my first calculus class didn't had a proof for that.

Does anybody have one? And most importantly, why e? Does that number represent anything special; is it a certain ratio like pi or anything like that? It really seem to be coming out of nowhere for me. The only definitions I've seen are all unintuitive: "e is defined as the integral from there to there of this" or "e is the number such that [such and such]", etc. But why does it appear in nature so often??

(If you know a similar thread exists, tell me because I didn't find one.)
 
Physics news on Phys.org
I think that there is significance in this relationship

1 = \int ^e _1 \frac {dx} x

Edit, fixed typo, now I'll add a bit of verbiage.

Think about that, the area under the inverse curve between 1 and e is equal to 1. This is a pretty fundamental definition of e.
 
Last edited:
Please do not double post.

See this thread.
 
Thread 'Is there a white hole inside every black hole?'
This is what I am thinking. How much feasible is it? There is a white hole inside every black hole The white hole spits mass/energy out continuously The mass/energy that is spit out of a white hole drops back into it eventually. This is because of extreme space time curvature around the white hole Ironically this extreme space time curvature of the space around a white hole is caused by the huge mass/energy packed in the white hole Because of continuously spitting mass/energy which keeps...
Back
Top