## [Computational Complexity] e to the pi vs pi to the e

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• (ANSWER to Trivia Questions from Last Post: The last president who became president NOT by being VP and having the prez die, but then did not run again, was
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(ANSWER to Trivia Questions from Last Post: The last president who became president NOT by being VP and having the prez die, but then did not run again, was Rutherford B. Hayes. Hayes and Obama are the only presidents who have law degrees from Harvard. For more on both of these questions see this excerpt from my Prez Trivia Quiz.)

When I was 12 my school got a very primitive computer. The teacher asked me what I wanted it to do for me. I said
I want to know whats bigger eπ or πe.
I typed both of them in, but I forgot the order I typed them in so I didn't find out. I didn't try again because I realized that even if I found out the answer it would not tell me a reason for the answer.

I had forgotten all about it until last week when I got a review of the book When Least is Best (book by Paul Nahim, review by Yannis Haralambous) in my capacity of SIGACT NEWS book review editor. Here is a quote from the review:
Imagine you are stranded on a desert island (without logarithm tables or computers) and--- probably due to an emotional shock---your only concern is to find out which one among numbers πe and eπ is bigger. The solution is: take h(x)=ln(x)/x, take the derivative twice to prove that x=e is a maximum, and that gives eπ is bigger.
I am sure this is well known; however, since I didn't know it until last week I hope this will enlighten some of my readers.

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Posted By GASARCH to Computational Complexity at 2/16/2010 09:54:00 AM
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