3Blue1Brown
Who cares about topology? (Inscribed rectangle problem)
This is an absolutely beautiful piece of math. It shows how certain ideas from topology, such as the mobius strip, can be used to solve a slightly softer form of an unsolved problem in geometry.
3Blue1Brown
Snell's law proof using springs: Brachistochrone - Part 2 of 2
A clever mechanical proof of Snell's law.
3Blue1Brown
Who cares about topology? (Inscribed rectangle problem): Topology - Part 1 of 3
This is an absolutely beautiful piece of math. It shows how certain ideas from topology, such as the mobius strip, can be used to solve a slightly softer form of an unsolved problem in geometry.
TED Talks
TED: Fractals and the art of roughness | Benoit Mandelbrot
At TED2010, mathematics legend Benoit Mandelbrot develops a theme he first discussed at TED in 1984 -- the extreme complexity of roughness, and the way that fractal math can find order within patterns that seem unknowably complicated.
3Blue1Brown
Cross products in the light of linear transformations: Essence of Linear Algebra - Part 11 of 15
The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.
PBS
Can You Solve the Poison Wine Challenge?
You're about to throw a party with a thousand bottles of wine, but you just discovered that one bottle is poisoned! Can you determine exactly which one it is?
TED-Ed
TED-ED: Can you solve the control room riddle? - Dennis Shasha
As your country's top spy, you must infiltrate the headquarters of the evil syndicate, find the secret control panel, and deactivate their death ray. But your reconnaissance team is spotty, and you have only limited information about the...
3Blue1Brown
The most unexpected answer to a counting puzzle
A puzzle involving colliding blocks where the number pi, vey unexpectedly, shows up.
TED Talks
William Noel: Revealing the lost codex of Archimedes
How do you read a two-thousand-year-old manuscript that has been erased, cut up, written on and painted over? With a powerful particle accelerator, of course! Ancient books curator William Noel tells the fascinating story behind the...
3Blue1Brown
Binary, Hanoi, and Sierpinski, part 2
How counting in Ternary can solve a variant of the Tower's of Hanoi puzzle, and how this gives rise to a beautiful connection to Sierpinski's triangle.
TED-Ed
TED-ED: Is our climate headed for a mathematical tipping point? - Victor J. Donnay
Scientists have warned that as CO2 levels in the atmosphere rise an increase in Earth's temperature by even two degrees could lead to catastrophic effects across the world. But how can such a tiny, measurable change in one factor lead to...
3Blue1Brown
What's so special about Euler's number e? | Essence of calculus, chapter 5
What is the derivative of a^x? Why is e^x its own derivative? This video shows how to think about the rule for differentiating exponential functions.
TED-Ed
TED-ED: Can you solve the buried treasure riddle? - Daniel Griller
After a massive storm tears through the Hex Archipelago, you find five grizzled survivors in the water. As an act of gratitude for saving them, they reveal a secret _ the island they were just on holds some buried treasure. But when the...
3Blue1Brown
Tattoos on Math
After a friend of mine got a tattoo with a representation of the cosecant function, it got me thinking about how there's another sense in which this function is a tattoo on math, so to speak.
3Blue1Brown
A Curious Pattern Indeed
Moser's circle problem. What is this pattern: 1, 2, 4, 8, 16, 31,...
3Blue1Brown
Who (else) cares about topology? Stolen necklaces and Borsuk-Ulam
How a famous theorem in topology, the Borsuk-Ulam theorem, can be used to solve a counting puzzle that seems completely distinct from topology.
3Blue1Brown
Why is pi here? And why is it squared? A geometric answer to the Basel problem
A beautiful solution to the Basel Problem (1+1/4+1/9+1/16+...) using Euclidian geometry. Unlike many more common proofs, this one makes it very clear why pi is involved in the answer.
SciShow
How Knots Help Us Understand the World
Knots are everywhere in our daily lives, but a new branch of mathematics is taking things to the next level.
TED Talks
TED: This company pays kids to do their math homework | Mohamad Jebara
Mohamad Jebara loves mathematics -- but he's concerned that too many students grow up thinking that this beautiful, rewarding subject is difficult and boring. His company is experimenting with a bold idea: paying students for completing...
PBS
Can We Hear Shapes?
Mathematician Mark Kac asked the question "Can we hear the shape of a drum?" It was a question that took over 20 years to answer. Sine waves, fundamental frequencies, eigenvalues, this episode has got it all!