Which is bigger: π^e or e^π?

Now that is math as art.

Fundamentally mathematics is a form only. :)

Generally, aᵇ > bᵃ if a is smaller than b, and both a & b are at least as big as e. So you can spot the answer in a heartbeat.

e^x=1+c+x^2/2+... For x>0, e^x>1+x Let x=pi/e-1 Then e^(pi/e-1)>pi/e Multiply by e e^(pi/e)>pi Raise to e power e^pi>pi^e

Great! How are you making these graphics?

WOW

Calista knows the answer not only for π^e or e^π Also for x^e or e^x, for any real number x👇

7

this has a flaw, the operator is not updating based on the value pi to the e is multiplication which means both directions equal the same value, but the flaw is that the operator is framing one larger than the other when it's simply not the case

e^π is bigger

π^e is bigger