A joke in approximating numbers raised to irrational powers
1–10 of 44 posts
Re: A joke in approximating numbers raised to irrational powers
#2for a second I thought 404 was the joke. Tried thinking hard for maybe 10 seconds to figure out why it was the joke, but then realized it was not.
Re: A joke in approximating numbers raised to irrational powers
#3for a second I thought 404 was the joke. Tried thinking hard for maybe 10 seconds to figure out why it was the joke, but then realized it was not.
An unfortunate mistake...
Re: A joke in approximating numbers raised to irrational powers
#4Reminds me of a cool proof I saw recently that there are two numbers a and b such that a and b are both irrational, but a^b is rational:
Take sqrt(2)^sqrt(2), which is either rational or not. If it's rational, we're done. If not, consider sqrt(2) ^ (sqrt(2) ^ sqrt(2)). Since (a^b)^c = a^bc, we get sqrt(2) ^ (sqrt(2))^2 = sqrt(2)^2 = 2, which is rational!
It feels like a bit of a sleight of hand, since we don't actually have to know whether sqrt(2)^sqrt(2) is rational for the proof to work.
Re: A joke in approximating numbers raised to irrational powers
#5Kinda weird that we don't get a graph for the final "solution"? I was looking forward to seeing how it compared to the other plots!
Re: A joke in approximating numbers raised to irrational powers
#6After following the correct link from @nomemory in the comments, this is good for a bit of a chuckle once you see the formula. If you can evaluate the formula you probably have a calculator or computer on hand and could compute the original value to double precision (I'm not even sure that the approximation would compute faster, but I didn't benchmark it).
But even though the approximation has no value in a real world application, the description of getting to the approximation is really good. I've never heard of Pade approximations before, and I liked the lead in from small angle approximations and Taylor series. I'd say this post is accessible to (and can be appreciated by) advanced undergraduates in engineering or math or comp sci.
Re: A joke in approximating numbers raised to irrational powers
#7Kinda weird that we don't get a graph for the final "solution"? I was looking forward to seeing how it compared to the other plots!
Good idea. I think I've rushed into publishing this. Anyway, I've reposted the link, and I will do the graph you've mentioned.
Re: A joke in approximating numbers raised to irrational powers
#8[flagged]
Re: A joke in approximating numbers raised to irrational powers
#9After following the correct link from @nomemory in the comments, this is good for a bit of a chuckle once you see the formula. If you can evaluate the formula you probably have a calculator or computer on hand and could compute the original value to double precision (I'm not even sure that the approximation would compute faster, but I didn't benchmark it). But even though the approximation has no value in a real worl…
https://news.ycombinator.com/item?id=42174105
New submission here.
Re: A joke in approximating numbers raised to irrational powers
#10[flagged]
[deleted]