Welcome to the Forum Archive!

Years of conversation fill a ton of digital pages, and we've kept all of it accessible to browse or copy over. Whether you're looking for reveal articles for older champions, or the first time that Rammus rolled into an "OK" thread, or anything in between, you can find it here. When you're finished, check out the boards to join in the latest League of Legends discussions.

Which of the quantities is greater, e^&#960; or &#960;^e?

e^&#960; 25 62.5%
&#960;^e 11 27.5%
They are equal 4 10%
Voters 40 .

For you Math Folks: WITHOUT A CALCULATOR, Which is Greater: e^π or π^e ?

Comment below rating threshold, click here to show it.

Mere Intricacy

Senior Member

2.7^3.14
or 3.14^2.7

2^3= 8
3^2=9

5^2=25
2^5=32

3^4=9x9 = 81
4^3= 16 x 4 = 64

Thus is guessing...
e^pi > pi^e

Comment below rating threshold, click here to show it.

Kodoku

Senior Member

The numbers are so close that you can't just take convenient approximations (like pi = 3) without introducing error greater than the difference between. I've typed up a proof, it requires some not entirely trivial calculus:

Edit: "product rule" should be "quotient rule".

Comment below rating threshold, click here to show it.

LouisLeGros

Senior Member

Thinking e was ~2.2 I guess wronged, probably would have guessed otherwise if I remembered that e was closer to 2.7

Comment below rating threshold, click here to show it.

Quision

Member

Quote:
Kodoku:
The numbers are so close that you can't just take convenient approximations (like pi = 3) without introducing error greater than the difference between. I've typed up a proof, it requires some not entirely trivial calculus:

Edit: &quot;product rule&quot; should be &quot;quotient rule&quot;.

That was actually pretty cool

Comment below rating threshold, click here to show it.

Mere Intricacy

Senior Member

Quote:
Kodoku:
The numbers are so close that you can't just take convenient approximations (like pi = 3) without introducing error greater than the difference between. I've typed up a proof, it requires some not entirely trivial calculus:

Edit: "product rule" should be "quotient rule".

Very nice!

Comment below rating threshold, click here to show it.

c4lm

Member

Put 0 thought into it and just assumed e^pi like any non nerdy person would.

Comment below rating threshold, click here to show it.