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3Blue1Brown
Visualizing quaternions (4d numbers) with stereographic projection
How to visualize quaternions, a 4d number system, in our 3d world
3Blue1Brown
But what is a Fourier series? From heat flow to circle drawings | DE4
Fourier series, from the heat equation to sines to cycles.
3Blue1Brown
Visualizing quaternions (4d numbers) with stereographic projection - Part 1 of 2
How to visualize quaternions, a 4d number system, in our 3d world
3Blue1Brown
What are quaternions, and how do you visualize them? A story of four dimensions.
How to think about this 4d number system in our 3d space.
3Blue1Brown
How (and why) to raise e to the power of a matrix | DE6
Exponentiating matrices, and the kinds of linear differential equations this solves.
3Blue1Brown
Quaternions and 3d rotation, explained interactively - Part 2 of 2
An introduction to an interactive experience on why quaternions describe 3d rotations
3Blue1Brown
Newton's Fractal (which Newton knew nothing about)
Newton's method, and the fractals the ensue
3Blue1Brown
But what is a Fourier series? From heat flow to circle drawings: Differential Equations - Part 4 0f 5
Fourier series, from the heat equation to sines to cycles.
3Blue1Brown
Quaternions and 3d rotation, explained interactively
An introduction to an interactive experience on why quaternions describe 3d rotations
3Blue1Brown
But what is the Fourier Transform? A visual introduction.
An animated introduction to the Fourier Transform, winding graphs around circles.
3Blue1Brown
But what is the Fourier Transform? A visual introduction.
An animated introduction to the Fourier Transform, winding graphs around circles.
3Blue1Brown
The Wallis product for pi, proved geometrically
A proof of the Wallis product for pi, together with some neat tricks using complex numbers to analyze circle geometry.
3Blue1Brown
All possible pythagorean triples, visualized
There are a few special right triangles many of us learn about in school, like the 3-4-5 triangle or the 5-12-13 triangle. Is there a way to understand all triplets of numbers (a, b, c) that satisfy a^2 + b^2 = c^2? There is! And it...
3Blue1Brown
Why does this product equal pi/2? A new proof of the Wallis formula for pi.
A new and more circularly proof of a famous infinite product for pi.
3Blue1Brown
But what is the Fourier Transform? A visual introduction.
An animated introduction to the Fourier Transform, winding graphs around circles.
3Blue1Brown
All possible pythagorean triples, visualized
There are a few special right triangles many of us learn about in school, like the 3-4-5 triangle or the 5-12-13 triangle. Is there a way to understand all triplets of numbers (a, b, c) that satisfy a^2 + b^2 = c^2? There is! And it uses...
3Blue1Brown
Visualizing the Riemann zeta function and analytic continuation
What is the Riemann zeta function? What is analytic continuation? This video lays out the complex analysis needed to answer these questions.
3Blue1Brown
Visualizing the Riemann hypothesis and analytic continuation
What is the Riemann zeta function? What is analytic continuation? This video lays out the complex analysis needed to answer these questions.
Curated Video
Basics of Complex Numbers and the Complex Number System Chart
In this video, we will define imaginary numbers and examine the complex number system.
Curated Video
Operations with Complex Numbers (add, subtract, multiply, and divide)
In this video, we learn how to add, subtract, multiply, and divide complex numbers. In the dividing portion of this video (7:05), we look at how to use the complex conjugate to rewrite quotients.
Curated Video
Complex Numbers in Polar Form
How do you write complex numbers in polar form? If they are in polar form, how do you rewrite them in argand or rectangular form? This video includes step by step instructions for converting complex values back and forth between these...
Curated Video
Complex Plane and Modulus
How do you plot points in the complex plane? How do you find modulus of a complex number? This video answers these questions by graphing points on the complex plane, defining modulus (absolute value), and calculating modulus.
Curated Video
Complex Numbers
“Complex Numbers” will explain what a complex number is and how to apply operations to complex numbers.