Cone and spacetime

Hi all,

Some of you were interested in the cone and spacetime. Here is a video from PBS introducing the topic.

Check it out and let me know if you have any questions!

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Random problem in sequence

Can you write a closed form of the following sequence:

1, 2,2, 3,3,3,4,4,4,4,…n,n,n,n,…,n,n (n copies), n+1, n+1,…..

This problem was cool enough for me that I wrote it on the cover of my mathematical analysis book from college. Have fun!

How to study math?

According to Paul Halmos (image from here):

study_math

Don’t just read it; fight it!¬†Ask your own questions,
look for your own examples, discover your own proofs.
Is the hypothesis necessary? Is the converse true?
What happens in the classical special case? What
about the degenerate cases? Where does the proof
use the hypothesis?

— Paul R. Halmos

Aliens and logical fallacy

This article reminds me of a problem on our quiz in Math 107 on logical fallacy. 

Here is another one if you are in the mood of finding logical fallacies. It is a true conversation I had with my husband Alan. 

Our tap has two settings and one of them has a particularly high pitch when the water is running. I didn’t like the high pitch noise and was in the mood of teasing Alan, so I said:” I don’t like that high pitch noise, but dolphins are fine with it. You are fine with it too, so you are a dolphin!”

Of course, Alan is not a dolphin. Can you point out the logical fallacy in the argument? 

Here is another logical fallacy called the Paradox of ravens. It certainly sounds funny at first glance. Try to resolve it? 

Happy Pi Day!!

Today is the \pi-day, and here are some cool things to check out:

Interview with Terence Tao from Numberphile.

If you like to estimate \pi yourself with the Monte Carlo method, this is a fun video to check out. Try to write a code and see how fast you get 100 digits of \pi.

Oh finally, eat some pie for sure.

Update: Just heard you can also compute \pi with coprime numbers. Here is a video.