[Intro Music] When you first learned about the pythagorean theorem that the sum of the squares of the two shorter sides on a right triangle always equals the square of its hypotenuse I’m guessing that you came to be pretty familiar with a few examples like the 3-4-5 triangle Or the 5-12-13 triangle, and I…

# Tag: three

## Cross products in the light of linear transformations | Essence of linear algebra chapter 11

Hey folks! Where we left off, I was talking about how to compute a three-dimensional cross product between two vectors, v x w. It’s this funny thing where you write a matrix, whose second column has the coordinates of v, whose third column has the coordinates of w, but the entries of that first column,…

## What they won’t teach you in calculus

3Blue1Brown [Classical music] Picture yourself as an early calculus student about to begin your first course: The months ahead of you hold within them a lot of hard work Some neat examples, some not so neat examples, beautiful connections to physics, not so beautiful piles of formulas to memorise, plenty of moments of getting stuck…

## Nonsquare matrices as transformations between dimensions | Essence of linear algebra, chapter 8

Hey, everyone! I’ve got another quick footnote for you between chapters today. When I talked about linear transformation so far, I’ve only really talked about transformations from 2-D vectors to other 2-D vectors, represented with 2-by-2 matrices; or from 3-D vectors to other 3-D vectors, represented with 3-by-3 matrices. But several commenters have asked about…

## But how does bitcoin actually work?

What does it mean to have a bitcoin? Many people have now heard of bitcoin, that’s it’s a fully digital currency, with no government to issue it and no banks needed to manage accounts and verify transactions. That no one actually knows who invented it. Yet many people don’t know the answer to this question,…

## Why is pi here? And why is it squared? A geometric answer to the Basel problem

I’m gonna guess that you have never had the experience of your heart rate increasing in excitement while you are imagining an infinitely large lake with lighthouses around it Well if you feel anything like I do about math, that is gonna change by the end of this video Take 1 plus 1/4 plus 1/9…

## Hilbert’s Curve: Is infinite math useful?

Let’s talk about space-filling curves. They are incredibly fun to animate and they also give a chance to address a certain philosophical question. Math often deals with infinite quantities, sometimes so intimately that the very substance of a result only actually makes sense in an infinite world. So the question is, how can these results…

## Pi hiding in prime regularities

This is a video I’ve been excited to make for a while. The story here braids together prime numbers, complex numbers and pi in a very pleasing trio. Quite often in modern math, especially that which flirts with the Riemann zeta function, these three seemingly unrelated objects show up in unison, and I want to…

## Ever wondered why slicing a cone gives an ellipse? Itâ€™s wonderfully clever!

Suppose you love math, and you had to choose just one proof to show someone to explain why math is beautiful. Something that can be appreciated by anyone from a wide range of backgrounds while still capturing the spirit of progress and cleverness in math. What would you choose? After I put out a video…

## But what is a Neural Network? | Deep learning, chapter 1

This is a three. It’s sloppily written and rendered at an extremely low resolution of 28 by 28 pixels. But your brain has no trouble recognizing it as a three and I want you to take a moment to appreciate How crazy it is that brains can do this so effortlessly? I mean this this…