Answering viewer questions about the index of refractionLessons are primarily funded directly by viewers, who get early access to new videos: https://3b1b.co/supportAn equally valuable form of support is to simply share the videos.Much of t

Understanding prisms requires understanding springs | Optics puzzles 3

Nov 30th, 2023 29m 24s

How the index of refraction arises, and why it depends on color.Quotebook Notebooks: https://3b1b.co/storeThese lessons are primarily funded directly by viewers: https://3b1b.co/supportAn equally valuable form of support is to simply share t

25 Math explainers you may enjoy | SoME3 results

Oct 7th, 2023 22m 12s

Playlist of all entries: https://www.youtube.com/playlist?list=PLnQX-jgAF5pQS2GUFCsatSyZkSH7e8UM8All non-video entries: https://some.3b1b.co/non-videosThank you to Jane Street, both for funding the event, and providing eager and able guest ju

Explaining the barber pole effect from origins of light | Optics puzzles 2

Sep 1st, 2023 21m 33s

Explaining the barber pole effect from the last video: https://youtu.be/QCX62YJCmGkNext video on the index of refraction: https://youtu.be/KTzGBJPuJwMHelp fund future projects: https://www.patreon.com/3blue1brownAn equally valuable form of s

The sugar water barber pole effect | Optics puzzles 1

Sep 1st, 2023 9m 57s

Shining polarized light into sugar water reveals diagonal stripes of color. Why?Next video: https://youtu.be/aXRTczANuIsSteve Mould's video on the topic: https://youtu.be/975r9a7FMqcHelp fund future projects: https://www.patreon.com/3blue1br

Wanna help judge SoME3?

Aug 18th, 2023 5m 55s

Enter as a judge here: https://some.3b1b.co/Last year's video about the Summer of Math Exposition: https://www.youtube.com/watch?v=cDofhN-RJqg------------------3blue1brown is a channel about animating math, in all senses of the word anim

A pretty reason why Gaussian + Gaussian = Gaussian

Jul 11th, 2023 13m 16s

A visual trick to compute the sum of two normally distributed variables.3b1b mailing list: https://3blue1brown.substack.com/Help fund future projects: https://www.patreon.com/3blue1brownSpecial thanks to these supporters: https://www.3blue1b

This pattern breaks, but for a good reason | Moser's circle problem

Jul 2nd, 2023 16m 13s

An apparent pattern that breaks, and the reason behind it.Summer of math exposition: https://3blue1brown.substack.com/p/some3-beginsLearn more at https://some.3b1b.co/Help fund future projects: https://www.patreon.com/3blue1brownAn equally

How They Fool Ya (live) | Math parody of Hallelujah

Jun 28th, 2023 4m

Happy Tau Day! Here's something a bit out of the ordinary for you.Thanks to Matt Parker, @standupmaths, for the invite.More about the event: https://festivalofthespokennerd.com/show/an-evening-of-unnecessary-detail/Thanks to Tim Blais, @aca

Convolutions | Why X+Y in probability is a beautiful mess

Jun 27th, 2023 27m 25s

Adding random variables, with connections to the central limit theorem.Help fund future projects: https://www.patreon.com/3blue1brownAn equally valuable form of support is to simply share the videos.0:00 - Intro quiz2:24 - Discrete case, d

Why π is in the normal distribution (beyond integral tricks)

Apr 2nd, 2023 24m 46s

Where's the circle? And how does it relate to where e^(-x^2) comes from?Help fund future projects: https://www.patreon.com/3blue1brownSpecial thanks to these supporters: https://www.3blue1brown.com/lessons/gaussian-integral#thanksAn equally

But what is the Central Limit Theorem?

Mar 14th, 2023 31m 15s

A visual introduction to probability's most important theoremHelp fund future projects: https://www.patreon.com/3blue1brownSpecial thanks to these lovely supporters: https://www.3blue1brown.com/lessons/clt#thanksAn equally valuable form of s

But what is a convolution?

Nov 18th, 2022 23m 1s

Discrete convolutions, from probability to image processing and FFTs.Video on the continuous case: https://youtu.be/IaSGqQa5O-MHelp fund future projects: https://www.patreon.com/3blue1brownSpecial thanks to these supporters: https://3b1b.co/

Researchers thought this was a bug (Borwein integrals)

Nov 4th, 2022 17m 26s

A pattern of integrals that all equal pi...until they don't.Next video on convolutions: https://youtu.be/KuXjwB4LzSAJohn Baez has a really fun article about this: https://johncarlosbaez.wordpress.com/2018/09/20/patterns-that-eventually-fail/

What makes a great math explanation? | SoME2 results

Oct 1st, 2022 17m 1s

Winners and honorable mentions for the SoME2 contestPlaylist of all entries: https://www.youtube.com/playlist?list=PLnQX-jgAF5pTZXPiD8ciEARRylD9brJXUHelp fund future projects: https://www.patreon.com/3blue1brownPost with links to all entrie

How to lie using visual proofs

Jul 3rd, 2022 18m 49s

Three false proofs, and what lessons they teach.New notebooks: https://store.dftba.com/collections/3blue1brown/products/mathematical-quotebook-notebookHelp fund future projects: https://www.patreon.com/3blue1brownAn equally valuable form of

Summer of Math Exposition 2 Invitation

Jun 9th, 2022 7m 14s

Announcing the second iteration of the Summer of Math Exposition Mailing-list: https://summerofmathexposition.substack.com/p/the-summer-of-math-exposition-is?s=rFind collaborators here: https://github.com/leios/SoME_Topics/Join the discord:

Olympiad level counting (Generating functions)

May 23rd, 2022 34m 36s

A lesson on generating functions, and clever uses of complex numbers for countingHelp fund future projects: https://www.patreon.com/3blue1brownAn equally valuable form of support is to simply share the videos.Special thanks: https://3b1b.co/

Oh, wait, actually the best Wordle opener is not “crane”…

Feb 13th, 2022 10m 53s

Following up on the Worlde-solver (https://youtu.be/v68zYyaEmEA), discussing a minor bug and more details about how the best first word was chosen.Special thanks to these supporters: https://3b1b.co/lessons/wordle#thanksHelp fund future proje

Solving Wordle using information theory

Feb 6th, 2022 30m 38s

An excuse to teach a lesson on information theory and entropy.Special thanks to these supporters: https://3b1b.co/lessons/wordle#thanksHelp fund future projects: https://www.patreon.com/3blue1brownAn equally valuable form of support is to si

A tale of two problem solvers (Average cube shadows)

Dec 20th, 2021 40m 6s

What's the average area of a cube's shadow?Numberphile video on Bertrand's paradox: https://youtu.be/mZBwsm6B280Help fund future projects: https://www.patreon.com/3blue1brownAn equally valuable form of support is to simply share the videos.

2021 Summer of Math Exposition results

Oct 23rd, 2021 12m 40s

Take a look at the full playlist (really): https://www.youtube.com/watch?v=fJWnA4j0_ho&list=PLnQX-jgAF5pTkwtUuVpqS5tuWmJ-6ZM-ZBlog post with more details: https://3b1b.co/some1-resultsThanks, as always, to the supporters of this channel for h

Beyond the Mandelbrot set, an intro to holomorphic dynamics

Oct 16th, 2021 27m 36s

An intro to holomorphic dynamics, the study of iterated complex functions.Video on Newton's fractal: https://youtu.be/-RdOwhmqP5sSpecial thanks to these supporters: https://3b1b.co/lessons/holomorphic-dynamics#thanksExtra special thanks to

From Newton’s method to Newton’s fractal (which Newton knew nothing about)

Oct 12th, 2021 26m 6s

Who knew root-finding could be so complicated?Next part: https://youtu.be/LqbZpur38nwSpecial thanks to the following supporters: https://3b1b.co/lessons/newtons-fractal#thanksAn equally valuable form of support is to simply share the videos.

The Summer of Math Exposition

Jul 16th, 2021 24m 21s

Announcement for the 2021 Summer of Math ExpositionPodcast/New channel: https://www.youtube.com/GrantSandersonDetails: https://3b1b.co/SoME1↓↓Things referenced through the video↓↓James Schloss:https://www.youtube.com/user/LeiosOSFree wi