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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

01-23-2013

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:

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".

That was actually pretty cool

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Mere Intricacy

Senior Member

01-24-2013

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!

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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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