First Educational Videos

Over winter break I decided to acquire a Wacom Bamboo tablet so that I could create educational videos/tutorials online and broadcast them via YouTube. The end goal is to host an abudance of creative calculus style videos that focus on conceptual understanding of the problems and a good source of examples a long with a range of extra materials to help the user.

Before I could do all that, I needed to experiment with the software/hardware and see what my possibilities are. Little did I know how difficult it was speaking to a camera and trying to get all the information out in a reasonable amount of time. So, on average, I’ve ended up spending an hour or so on a ~10 minute physics problem transferring about half of the information that I wanted to get to the user. With that being said, my confidence is growing and my knowledge about the tools is progressing. It’s also been a hell of a study tool for me.

Here are my first two videos. Hopefully they are the start of a very long project that ends up helping many people understand mathematics and physics. Feel free to leave a comment here or on YouTube if you have a suggestion for me.

Three Step One Dimensional Kinematics Equation Problem

Two-Dimensional Kinematics Problem

Well… there a start…

Proof that 2=1… or not

Federico Pistono posted about the Wall Street Journal’s opinion piece on science proving the existence of God… or not, so I am going to post (in similar fashion) 2=1… or not.

Many involved with mathematics have already heard of this fallacious proof, however it is an eloquent one and I wanted to share it:

Objective: To prove that all numbers equal each other, namely, 2=1.

Proof

1. Let a and b be equal non-zero numbers.
a=b

2. Multiply both sides by a
a^2=ab

3. Add a^2-2ab to both sides
a^2+a^2-2ab=ab+a^2-2ab

4. Factor:
2(a^2-ab)=a^2-ab

5. Divide both sides by a^2-ab
2=1

Ah, brilliant, we have just proved step-by-step that 2 is equal to 1. Using these same steps we can prove that any number is equal to each other, right?

Well, obviously, there is something deeply wrong about this proof. Try to consider what might be wrong for a moment, it is a fun challenge. When you’ve done that, continue reading.

Lame_Math_Joke_by_ichiko_wind_griffin

The problem in this fallacious proof lies in step 5. In step 1 we stated that a=b, so dividing by a^2-ab would mean we would be dividing by 0. Strange things happen when you divide by 0, and this result is one of them. Therefore, this proof is invalid and 2 does not equal 1. Mathematics is still fundamentally sound and all can remain at peace.