What is a Fourier Series? (Explained by drawing circles) - Smarter Every Day 205 | Summary and Q&A

TL;DR

Waves can be added together to create complex functions, such as the Fourier Series, which has applications in physics and mathematics.

Key Insights

• 👋 Sine waves can be added together using the Fourier Series to create more complex functions.
• ❓ Doga's visualizations of the Fourier Series using animation provide a clear and beautiful representation of the concept.
• 👋 The ability to create any function using the Fourier Series demonstrates the power and versatility of waves in mathematics and physics.
• 🍉 Mathswagger, a term coined in the video, refers to the confidence and abilities of someone skilled in mathematics.
• 😌 The beauty of math lies in its ability to describe the physical world and approximate any phenomenon.
• 🤗 Kiwi Co. sponsors Smarter Every Day, a YouTube channel that promotes hands-on learning and building projects with children.
• 👶 Kiwi Co. offers subscription boxes with various project kits for children, aimed at fostering creativity and problem-solving skills.

Transcript

• What up? Today we're gonna talk about waves. This is a circle, you probably knew that. If we were to turn this circle on and watch it go up and down and up and down and trace that motion out, you get what's called a sine wave, which you know to be important in things like pendulum motion, particle physics, things of that nature. Sine waves are im... Read More

Questions & Answers

Q: How do sine waves and square waves differ?

Sine waves are smooth and continuous, while square waves have sharp edges. Sine waves are considered the simplest form of wave, while square waves are slightly more complex.

Q: Can you explain how Doga used curvy waves to create sharp-edged square waves?

Doga added together different oscillations or simple harmonic motion to create square waves. By stacking curvy waves (also known as wipers), he was able to generate sharp-edged square waves.

Q: How did Doga visualize the Fourier Series?

Doga used Mathematica, a software program, to visualize the Fourier Series. He created a table of animations and exported them as GIFs.

Q: How can the Fourier Series be used to create complex functions?

The Fourier Series allows for the creation of any function by adding together multiple simple harmonic motion components. By stacking circles and sine waves, complex functions can be accurately represented.

Summary & Key Takeaways

• Waves, such as sine waves and square waves, can be added together using the Fourier Series to create more complex functions.

• A student from Georgia Tech, Doga, developed a visual representation of the Fourier Series using animation, which helped explain the concept in a simple and beautiful way.

• The ability to create any function using the Fourier Series demonstrates the power of waves and the underlying mathematics.