## Which of the quantities is greater, e^π or π^e?

e^π 25 62.50%
π^e 11 27.50%
They are equal 4 10.00%
Voters: 40. You may not vote on this poll

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

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

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".

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

Quision

Member

Quote:
Originally Posted by 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

Mere Intricacy

Senior Member

Quote:
Originally Posted by 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!

c4lm

Member

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