How to Defeat a Mathematician #shorts

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This works 100% of the time. #shorts

Here's a silly video about approximations. It's not meant to be taken seriously, but some of the content in it is definitely worth checking out if you don't know about it already!

For example, the small angle approximation is briefly mentioned, which is where for very small angles, the value of sine and tangent are approximately equal to the angle itself. Similarly, for cosine, we use a truncated version of its Taylor series in the small angle approximation.

This approximation is immensely helpful in approximating solutions to difficult systems in physics. For example, a differential equation showing how pendulums behave, even in a very basic system, contains a sine term that makes the equation difficult to solve. However with the small angle approximation, the equation becomes very similar to the simple harmonic motion equation, which we do know how to solve.

So although approximations don't give us exact answers, they are extremely useful in solving problems we wouldn't otherwise know how to tackle.

... and then there's good old π = 3. We don't talk about that.

The music in the background is (again) something I threw together just for this video. I will post a playthrough of it over on my second channel in the next few days - link to my channel is below!

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