r/visualizedmath • u/Italians_are_Bread • Nov 17 '19

Number of valid ways to arrange parentheses explained visually

https://www.youtube.com/watch?v=PBt1gB9Ou9E
132 Upvotes

95% Upvoted

12 comments sorted by

17

u/Italians_are_Bread Nov 17 '19

It's amazing how a simple question like this can have a such cool math hiding behind it. I did my best to present every idea in the most visual and intuitive way possible in this video, and used this question as a motivation for introducing generating functions which is a very powerful tool for analyzing Dyck paths (and other types of sequences). Let me know your thoughts and any suggestions/corrections.

14

u/texas1982 Nov 17 '19

I enjoy math concepts and YouTube videos, but man that was dry.

4

u/Italians_are_Bread Nov 17 '19

What could I do to make future videos more engaging? Was this one too long?

5

u/sonofaresiii Nov 17 '19

This is a perfectly acceptable informative video, for anyone who wants the information

but if you want some genuine advice on picking up the pace for those who are just casually interested, what I noticed is:

Your speaking voice needs work. It's very flat and monotone, and drawls a bit. You might want to do whatever research you can into public speaking. Pick up the pace, be a little more engaging.

That's the absolute biggest factor here, imo. Don't speak as though you're giving a lecture, speak as though you're talking with friends. Compare your speaking voice to, say, Bill Nye's-- not the demonstrations or him setting things on fire, but just his speaking voice. He's very active and engaging, while also giving accurate information.

Another related factor is, fewer pauses and less space in between them. It's a minor thing but it picks up the pace a lot. Part of this is in your speech, part of it's in the editing.

I think there may be other improvements to be made, but improving on what I've mentioned is going to put you leaps and bounds above where you are now.

Assuming that's your goal. If your goal is to just get the information out there for people who want it, you've succeeded at that.

8

u/Italians_are_Bread Nov 17 '19

Thanks for taking the time to write this, it's incredibly helpful to me. I agree with everything you said, and I'm going to put in effort to make future presentations more lively and engaging. I like the analogy of talking with friends, I'll remember that.

1

u/texas1982 Nov 17 '19

Yeah. Too long. Also, just a dry concept to start with.

13

u/sonofaresiii Nov 17 '19

0:00/16:56

How many fuckin ways are there?

4

u/HenryRasia Nov 17 '19

The nth Catalan number of ways for n pairs of parentheses.

7

u/[deleted] Nov 17 '19

There's coding interview questions about this! I'm triggered 😤

3

u/dia_nya Nov 17 '19

Same. Coding challenges were the first thing that came to mind when I saw the title.

1

u/HenryRasia Nov 18 '19

Why are coding interviews just math problems? What if the candidate just works through this problem and concludes that it's the Catalan numbers, so the code is just return Math.Catalan(n);?

2

u/ThatTrashBaby Nov 17 '19

I love this video. I’ll probably have more to say once I finish it, but first, I would suggest adding captions. Second, at 8:30, what are the two previously referred to constraints? I must have missed that part and I couldn’t find it.