## Sine waves explained through a story

Hi I’m Toby and welcome back to the Joy of Mathematics, I’m so glad you could join me today. I’ll run some ideas across the bottom of the screen that we are going to encounter during a story today. I’d also like to thank this episode’s sponsor Brilliant.org. So today’s story is another one about

## What is quantum mechanics really all about?

For the most part, physics is a pretty straightforward discipline. While the math might be complicated, physics is often about quantifying such things as “what goes up, must come down” and “don’t play chicken with a train.” Statements like those are intuitive and pretty much everyone can get their head around them. But, over the

## Creating Circular Motion from Sine and Cosine Curves

Mr. P: Good morning. Let’s start with a dot moving in the y-direction in simple harmonic motion, just like a vertical mass spring system. Flipping Physics If we set the dot in motion at a constant velocity to the right, Bo what sort of function does that create? Bo: That looks just like a sine

## Fourier Transform, Fourier Series, and frequency spectrum

We have an X axis and a Y axis. Let us also create an axis that represents the angle theta. The green line rotates by the angle theta. For each value of theta, the X coordinate represents the cosine of theta, and the Y coordinate represents the sine of theta. The angle theta can range

## Why sin and cos don’t mean anything

This is candy. It’s called candy because it was originally from India, where sugar cane was first processed into sugar crystals around the 4th century AD, with a piece of sugar referred to as ‘khanda’ (खण्ड) in Sanskrit. *Simon surreptitiously deposits the candy into his mouth* Now, as the knowledge of the cultivation and processing