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

e^π 25 62.5%
π^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 ?

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Mere Intricacy

Senior Member

01-23-2013

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


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Kodoku

Senior Member

01-23-2013

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".


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LouisLeGros

Senior Member

01-24-2013

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


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Quision

Member

01-24-2013

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".

That was actually pretty cool


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Mere Intricacy

Senior Member

01-24-2013

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!


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c4lm

Member

01-24-2013

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


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vcadoda

Senior Member

01-24-2013

Well got that wrong


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