Be Smart
Why Nature Loves Hexagons (featuring Infinite Series!)
From spirals to spots to fractals, nature is full of interesting patterns. Many of these patterns even resemble geometric shapes. One of the most common? Hexagons. Why do we see this six-sided shape occur so many times in nature? This...
PBS
Why the Universe Needs Dark Energy
We know the universe will continue to expand forever, so now we can begin to complete the first Friedmann equation, and determine the shape and geometry of our universe. At first glance, it would seem that the equation doesn't quite add...
PBS
Proving Brouwer's Fixed Point Theorem
There is a proof for Brouwer's Fixed Point Theorem that uses a bridge - or portal - between geometry and algebra.
TED-Ed
TED-Ed: Pizza physics (New York-style) - Colm Kelleher
People love eating pizza, but every style of pie has a different consistency. If "New York-style"--thin, flat, and large--is your texture of choice, then you've probably eaten a slice that was as messy as it was delicious. Colm Kelleher...
MinutePhysics
Extraterrestrial Cycloids - Why Are They on Europa?
Thanks to the James Webb Space Telescope (JWST) and Space Telescope Science Institute for supporting this video. This video is about the cycloid curves on Jupiter's moon Europa - they're ridges or valleys in the icy surface that formed...
TED-Ed
TED-ED: The complex geometry of Islamic design - Eric Broug
In Islamic culture, geometric design is everywhere: you can find it in mosques, madrasas, palaces, and private homes. And despite the remarkable complexity of these designs, they can be created with just a compass to draw circles and a...
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...
PBS
Can a Circle Be a Straight Line?
On this week's episode of Spacetime, Gabe talks about what it actually means for a line to be straight so we can better understand what we mean by the idea of "curved Spacetime". This is Part One of our series on General relativity, so...
TED-Ed
TED-ED: The mighty mathematics of the lever - Andy Peterson and Zack Patterson
Archimedes once said "Give me a place to stand, and I shall move the Earth." While the idea of a person moving such a huge mass on their own might sound impossible, chances are you've seen this idea in action at your local playground....
3Blue1Brown
But WHY is a sphere's surface area four times its shadow?
Two proofs for the surface area of a sphere
3Blue1Brown
What does genius look like in math? Where does it come from? (Dandelin spheres)
A beautiful proof of why slicing a cone gives an ellipse.
SciShow
How Can the Universe Be Flat?
Can geometry predict the future? Cosmologists think the overall curvature of universe can tell us secrets about how it will eventually end.
TED-Ed
TED-Ed: Why are manhole covers round? - Marc Chamberland
Why are most manhole covers round? Sure it makes them easy to roll, and slide into place in any alignment. But there's another, more compelling reason, involving a peculiar geometric property of circles and other shapes. Marc Chamberland...
TED-Ed
TED-ED: A brief history of banned numbers - Alessandra King
They say the pen is mightier than the sword, and authorities have often agreed. From outlawed religious tracts and revolutionary manifestos to censored and burned books, we know the potential power of words to overturn the social order....
3Blue1Brown
But why is a sphere's surface area four times its shadow?
Two proofs for the surface area of a sphere
TED-Ed
The unexpected math of origami | Evan Zodl
Origami, which literally translates to "folding paper," is a Japanese practice dating back to at least the 17th century. In origami, a single, traditionally square sheet of paper can be transformed into almost any shape, purely by...
SciShow
What If the Universe Was Shaped Like a Donut?
The universe could be a donut in a fourth spatial dimension. Which would mean that we could potentially see our own galaxy repeated from the past... Our 3D brains aren't ready for this.
TED-Ed
TED-ED: The real story behind Archimedes' Eureka! - Armand D'Angour
When you think of Archimedes' Eureka moment, you probably imagine a man in a bathtub, right? As it turns out, there's much more to the story. Armand D'Angour tells the story of Archimedes' biggest assignment -- an enormous floating...
TED-Ed
TED-ED: How to prove a mathematical theory - Scott Kennedy
Euclid of Alexandria revolutionized the way that mathematics is written, presented or thought about, and introduced the concept of mathematical proofs. Discover what it takes to move from a loose theory or idea to a universally...
SciShow
π 'N' Science
It's pi day! Hank explains why this irrational number is important to scientists, and discusses a bit of a controversy that surrounds it.
TED-Ed
TED-Ed: The mathematical secrets of Pascal's triangle - Wajdi Mohamed Ratemi
Pascal's triangle, which at first may just look like a neatly arranged stack of numbers, is actually a mathematical treasure trove. But what about it has so intrigued mathematicians the world over? Wajdi Mohamed Ratemi shows how Pascal's...
TED-Ed
TED-Ed: Is math discovered or invented? - Jeff Dekofsky
Would mathematics exist if people didn't? Did we create mathematical concepts to help us understand the world around us, or is math the native language of the universe itself? Jeff Dekofsky traces some famous arguments in this ancient...
MinutePhysics
TOP 10 REASONS Why We Know the Earth is Round
TOP 10 REASONS Why We Know the Earth is Round
3Blue1Brown
Why slicing a cone gives an ellipse
A beautiful proof of why slicing a cone gives an ellipse.