The dynamics of e^(πi) // TRAIN BRAIN

The dynamics of e^(πi)

A fuller version of this explanation, also including the reason we care about complex exponents in the first place: https://youtu.be/-j8PzkZ70Lg

3Blue1Brown

3blue1brown, by Grant Sanderson, is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective. Contact and F...

The dynamics of e^(πi)

But what is a Laplace Transform?

The dynamics of e^(πi)

How AI connects text and images

The AI that solved IMO Geometry Problems | Guest video by @Aleph0

But how do AI videos actually work? | Guest video by @WelchLabsVideo

Summer of Math Exposition #4 | Teachers, I'd love to hear from you

Where my explanation of Grover’s algorithm failed

But what is Quantum Computing? (Grover's Algorithm)

Testing your intuition for quantum computing

How to measure nearby galaxies

Measuring the distance to Venus without radar

Measuring the speed of light using Jupiter's moons

The tragic tale of Guillaume Le Gentil

Zooming out by powers of 10

There's more to those colliding blocks that compute pi

When being beautifully wrong leads to discovery

Why the ancient Greek's rejected heliocentrism

How to estimate the distance to the sun

How Aristarchus deduced the distance to the moon

The cosmic distance ladder with Terence Tao, part 2

How Earth's size was computed by Eratosthenes

Measuring the earth with Terence Tao

The space of all musical intervals

The barber pole optical mystery

Monge's Theorem

Thinking through double slits

The inscribed square problem

The meaning within the Mandelbrot set

The scale of training LLMs

This puzzle is tricker than it seems

The Triangle Of Power

The twirling tiles puzzle

Why 4d geometry makes me sad

LLMs are next-word predictors

Hologram preview

Holograms are wild

In the vector space of all advice...

Temperature in LLMs

Simulating the electric field and a moving charge

How the Mandelbrot set is defined

A challenging puzzle about subset sums

Ellipses have multiple definitions, how are these the same?

Three levels of understanding Bayes' theorem

The medical test paradox (well "paradox")

Positioned as the hardest question on a Putnam exam (#6, 1992)

Why does light slowing imply a bend? (Beyond the tank/car analogy)

The cube shadow puzzle

What does it mean that light "slows down" in glass?

Why do we call them "scalars"?

A beautiful international math olympiad problem

Definition of a "bit", in information theory

The Newton art puzzle

What is a group?

How to derive a formula for π

The limit of limiting arguments

For anyone who might not know how links in shorts work

Infinite Lighthouses and π

"Proof" of a sphere's surface area

Can you even imagine 2^256?

Order from chaos

The surface area of a sphere

A short on shorts

A pretty way to add weighted dice

Image blurring

These integrals all equal π, until...

The split necklace puzzle (with a surprise topological solution)

Error correction is incredible

The chessboard and coins puzzle

Prime spirals

The barber pole effect

Fourier series

Seeing with sound

The standard explanation of a prism falls short

I'm still astounded this is true

Don't let it fool you!

Prime spirals

X-rays "faster" than the speed of light, and more refractive index questions | Optics puzzles part 4

You can't explain prisms without understanding springs | Optics puzzles part 3

The origin of light, scattering, and polarization | Barber pole, part 2