Essence of linear algebra - "[Grant Sanderson of 3Blue1Brown (now at Khan Academy) animates] the geometric intuitions underlying linear algebra, making the many matrix and vector operations feel less arbitrary." [more inside]
Compass-and-straightedge construction (aka Euclidean construction) is a method of drawing precise geometric figures using only a compass and a straightedge (like a ruler without the markings). MathOpenRef maintains a catalog of many common constructions, each with an explanatory animation and a proof. This YouTube video demonstrates how to construct almost every polygon that can be constructed using these methods. [more inside]
Understanding e to the pi i - "An intuitive explanation as to why e to the pi i equals -1 without a hint of calculus. This is not your usual Taylor series nonsense." (via via; reddit; previously) [more inside]
"It's just one of those days where you wake up thinking that if you jazzed up Stravinsky's Owl And The Pussycat it'd be awesome..." [SLYT] [more inside]
The series of Project Mathematics tapes regularly brought the house down at the annual SIGGRAPH video show; these mathematical animations were glowing jewels among the over-produced, techy-commercial animations usually shown at SIGGRAPH. -- Edward Tufte via edwardtufte.comI wonder where these jewels might be found ... [more inside]
Ahead of Pi Day (March 14), Matt Parker tries to accurately calculate pi using pies. [SLYT] An extended version of the video will be uploaded on Pi Day, but here's your chance to go out and buy pies before that. (Video runs 3 minutes, 14 seconds.)
Henry Reich of Minute Physics shares his favorite science blogs, video channels, and other resources on the web. (Minute Physics previously) [more inside]
Numberphile is a website containing short videos (approx. 5-10 min.) about numbers and stuff. Mathematicians and physicists play around with the tools of their trade and explain things in simple, clear language. Learn things you didn't know you were interested in! Find out why 493-7775 is a pretty cool phone number! What's the significance of 42, anyway? What the heck is a vampire number? Why does Pac-Man have only 255 screens? Suitable for viewing by everyone from intelligent and curious middle-schoolers to math-impaired adults. Browse their YouTube channel here. (Via)
Robert MacPherson interviewed as part of the Simons Foundation's Science Lives series. MacPherson is among the founders of the modern theory of singularities, points like a kink in a curve where the geometry of a space stops being smooth and starts behaving badly. In the interview, MacPherson talks about cultural differences between math and music, his frustration with high school math, growing up gay in the South and life as a gay man in the scientific community, smuggling $23,000 in cash into post-Soviet Russia to help mathematicians there keep the lights on, catastrophe theory, perverse sheaves, how to be a successful graduate student, stuttering, and of course the development of the intersection homology theory for which he is most well-known.
We've discussed subblue/Tom Beddard and Mandlebulbs before, but two months ago L'Eclaireur Sévigné asked him to create a few animations for their 147-screen exhibition. And here are the hypnotic, terrifying results.
Let's say you're me and you're in math class, and you're supposed to be learning about factoring. Trouble is, your teacher is too busy trying to convince you that factoring is a useful skill for the average person to know with real-world applications ranging from passing your state exams all the way to getting a higher SAT score and unfortunately does not have the time to show you why factoring is actually interesting. It's perfectly reasonable for you to get bored in this situation. So like any reasonable person, you start doodling.[more inside]
Futurama has always been a haven for geek humor, but last week's episode "The Prisoner of Benda" pushed things to the next level. First hinted at in an American Physical Society interview with showrunner David X. Cohen (previously), staff writer and mathematics Ph.D. Ken Keeler devised a novel mathematical proof based on group theory to resolve the logic puzzle spawned by the episode's brain-swapping (but no backsies!) conceit. Curious how it works? Read the proof (in the show or in plain text), then see it in action using this handy chart. Too much math for a lazy Sunday? Then entertain your brain with lengthy clips from the episode -- including two of the funniest moments in the series in the span of two minutes.
Douglas Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid has been recorded as a series of video lectures for MIT's Open Courseware project.
A talk with Benoît Mandelbrot, entitled Fractals in Science, Engineering and Finance (Roughness and Beauty) [video, 80mins, realplayer] about fractals as A Theory of Roughness.