Hi everyone, so it is my birthday today and coincidentally I just reached 100
subscribers on YouTube so I'm really excited about that. That means that I can
now have a custom URL so you can now find me at youtube.com/thawom
that's the acronym of The How and Why of Mathematics. I love this banner because
when you scroll down a bit it's like "I'm watching you." Okay so there's that
custom URL now, and I just wanted to give a big thank you to my first 100
subscribers. You guys have been so nice; some of you have left some really
wonderful comments for me which always make my day. So I wanted to give a big
thank you and also tell you about some upcoming videos that I'm planning to
make and get your opinions on what I should focus on. So these are some of the
ideas I had for videos to make in 2019. So in addition to these also just let me
know in the comments any mathematical topics that you're struggling with or
any questions that you can't figure out that you'd like me to make videos on. So
I'm happy to do whatever requests you want. So obviously I'm going to finish
the unit circle series and the one about trig equations, so that one should be
quite interesting. I think that those techniques are just so useful, the unit
circle techniques that Dr. Hoffman taught me, because they're just so much easier
than what they're teaching in school at the moment with like the ASTC
mnemonic and all that stuff, so I will definitely finish that very soon. Also
I'm gonna keep going, keep making questions on the Australian mathematics
competition and I thought I might branch out into like Olympiad questions.
There's like the International Olympiad stuff, other questions that I can
find that are a bit harder so I might go over some of those. Now
something that I've been wanting to talk about for a long time is how calculators
actually work, because this was something that I was very curious about in school,
like how does a calculator actually know what sine of 40 degrees is
and stuff like that. And also how did people do these calculations before there
were calculators. So there's all this really interesting history about like how
people calculated pi, how people made sine tables and cosine tables and so on,
and stuff like prosthaphaeresis and all the work that Napier did, all that
stuff is quite interesting, so I thought I might make some videos on that. So when I
was a kid I used to play these LucasArts adventure games all the time, where you'd
have to like figure out how to use stuff you picked up and like it was sort of
like puzzle solving basically so I used to play these all the time and I noticed
that the kind of strategies that I used to use to solve the puzzles in these
games were very similar to some of the strategies that I use to solve
mathematical problems, so I thought that I could do a video on what video games
taught me about mathematics. So this would be like just a general look at
various problem-solving strategies that you can use for mathematics. You can
tell how old I am by the fact that this game fits in such a tiny fraction of the
screen, but this is what video games used to
look like back when I was a kid. So the video that I made on PEMDAS and that
viral facebook question is one of my most popular videos by far and I've
learned a lot since then particularly, about how calculators handle expressions
like those and I realized that the issue is actually kind of a lot more important
than you would think from just a being this silly Facebook question because
check this out! Different models of calculator will calculate things
differently with the same expression, because they're following different
orders of operations. Now that could really trip someone up in an exam, like
you could use lose marks if you didn't realise that your calculator doesn't
follow the rules that you're used to. So I definitely want to make a follow-up video
to the PEMDAS one, about how calculators handle these expressions, and how we got
to this point where different models of calculators are giving different answers
to the same question. I also thought that I might make a video about how I create
mathematical diagrams which is through a program called metapost which is like a
programming language for diagrams. And I wrote this program called mpsketch
a while ago, which just lets you sort of draw paths on and then it will tell you
the metapost code to create that, so that makes it much much more
easy to use. So I thought that I should make a video about that. So let me know
in the comments which of those video ideas you're interested in and if
there's any other topics that you want me to cover then let me know. And just
thank you so much to everyone who's subscribed so far, you guys have been
wonderful!