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Archive for January, 2017

I found a question on mathoverflow, it asks “is there  exists irrational numbers a and b such that a^b is rational”.

Obviously, if you let a=e, b=\log 3, then a^b=e^{\log 3}=3 is rational.

But someone gave a very interesting proof.

screenshot_2017-01-03_15-40-30

You don’t have to know whether \sqrt{2}^{\sqrt{2}} is rational or not, you can just get the answer. That is a clever trick.

 

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I found a quite interesting site http://memtropy.com/proofs-without-words/, if you can understand what it says, click it and see more.

proofwithoutwords1

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Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao