Snowy Mathematical Art from Simon Beck
Simon is an artist and is most well-known for making incredibly delicate and detailed art in the snow, just by walking over a fresh snowfall. He literally walks miles in the snow to create these pieces. He could spend hours upon hours creating one design, just to have it be covered by snowfall or blown away by the next day. But he still makes them.
These delicate patterns were created in the beautiful Savoie Valley in France, overlooking Mont Blanc.
He creates large, mathematical patterns that have different effects when viewed from different angles.
Source: viralnova.com Images: Simon Beck
These photos are shadowgraphs of a hydrogen flame exploding inside a balloon. The shadowgraph optical technique highlights density and temperature variations through their effect on a fluid’s refractive index. Here we see that the hydrogen flame has a strong cellular structure and is more turbulent than a methane flame. The cellular structure is a sign of an instability in the curved flame front. The instability and accompanying cellular appearance are a result of the complicated transport and reaction of fuel and oxidizer inside the flame. (Photo credits: P. Julien et al.)
The truth has nothing to fear from inquiry. Be wary of anyone who would discourage questions.
Ann Friedman's Disapproval Matrix for handling criticism is a thing of genius, not to mention essential internet-age literacy. She explains:
Critics: These are smart people who know something about your field. They are taking a hard look at your work and are not loving it. You’ll probably want to listen to what they have to say, and make some adjustments to your work based on their thoughtful comments.
Lovers: These people are invested in you and are also giving you negative but rational feedback because they want you to improve. Listen to them, too.
Frenemies: Ooooh, this quadrant is tricky. These people really know how to hurt you, because they know you personally or know your work pretty well. But at the end of the day, their criticism is not actually about your work—it’s about you personally. And they aren’t actually interested in a productive conversation that will result in you becoming better at what you do. They just wanna undermine you. Dishonorable mention goes to The Hater Within, aka the irrational voice inside you that says you suck, which usually falls into this quadrant. Tell all of these fools to sit down and shut up.
Haters: This is your garden-variety, often anonymous troll who wants to tear down everything about you for no rational reason. Folks in this quadrant are easy to write off because they’re counterproductive and you don’t even know them. Ignore! Engaging won’t make you any better at what you do. And then rest easy, because having haters is proof your work is finding a wide audience and is sparking conversation. Own it.
The general rule of thumb? When you receive negative feedback that falls into one of the top two quadrants—from experts or people who care about you who are engaging with and rationally critiquing your work—you should probably take their comments to heart. When you receive negative feedback that falls into the bottom two quadrants, you should just let it roll off your back and just keep doin’ you.
This chart shows how to solve every quartic polynomial.
Notice it also shows how to solve cubics and quadratics, but it can’t be improved to quintics (polynomials of degree five) or higher, because only polynomials with degree less than five can be solved algebraically in general: this is the Abel-Ruffini theorem. Some specific quintics can be solved, but the method is far more tedious. In 2004 Daniel Lazard wrote out a three-page formula for the roots of a general solvable quintic.
Popping a balloon filled with mercury.
The structure of an animal cell