I was avoiding my trig homework and watching anime when - NO WHAT IS THIS? WHY ARE THEY DOING DOUBLE ANGLE IDENTITIES I THOUGHT THEY WERE FIRST YEARS IN HIGH SCHOOL
Never punish a geek.
using namespace std;
for ( int count = 1; count <= 500; count++)
cout « “I will not throw paper airplanes in class.” « endl;
You (yellow), need to pass the red ball to your friend (blue), as you both sit on a merry-go-round. I posted a similar animation of this problem before- and this one shows quite an extreme of the solution. You can only throw the ball very slowly, so you throw the ball to where your friend will be when it gets to them. From above, the ball travels in a straight line, but in the world of the spinning merry-go-round that you occupy- the ball seems to be warped on a curve by some invisible forces. These invisible forces are called the Coriolis and Centrifugal effects. [code] [more]
- for the purpose of understanding how this works we are going to imagine that something is trying pull an up quark from a proton which is made from 2 ups and 1 down quark.
- As you try to pull the up quark from the proton a tube of energy is formed between the proton and the up quark.
- eventually the tube of energy becomes enough for matter-anti-matter creation with an up and an anti-up quark.
- the up quark goes back to the proton meaning that the proton has always stayed whole and the anti-up quark joins the up quark that was separated from the proton to create a meson.
- this means that is is impossible to ever have a quark by itself.
- the quarks themselves are make up 8MeV while quark confinement generates about 930MeV meaning that most of our mass actually comes from quark confinement.
Mathematician Maryam Mirzakhani is the first woman to win a Fields Medal. It had been an all-boys club since the prizes were established in 1936.
Mirzakhani, a native of Iran, is a professor at Stanford University. She won for her work on “the dynamics and geometry of Riemann surfaces and their moduli spaces.”
Here’s how Nature summed up her contributions:
“Perhaps Maryam’s most important achievement is her work on dynamics,” says Curtis McMullen of Harvard University. Many natural problems in dynamics, such as the three-body problem of celestial mechanics (for example, interactions of the Sun, the Moon and Earth), have no exact mathematical solution. Mirzakhani found that in dynamical systems evolving in ways that twist and stretch their shape, the systems’ trajectories “are tightly constrained to follow algebraic laws”, says McMullen. He adds that Mirzakhani’s achievements “combine superb problem-solving ability, ambitious mathematical vision and fluency in many disciplines, which is unusual in the modern era, when considerable specialization is often required to reach the frontier”.
Erica Klarreich wrote a wonderful summary of Dr. Mirzakhani for Quanta magazine, which is worth a read. She’s apparently quite the generalist — deriving intellectual satisfaction in “crossing the imaginary boundaries people set up between different fields.” Among her diverse body of work outside dynamics is her doctoral dissertation on geodesics of hyperbolic surfaces, which another researcher called “the kind of mathematics you immediately recognize belongs in a textbook.” Meanwhile, she’s an unassuming character herself, with a deep love of her work and a phenomenal work ethic: “You have to spend some energy and effort to see the beauty of math.”