Quasicoherent

A blog about math and code that sometimes makes sense.

• Surprising Positive Semidefiniteness

They say that in Euclidean geometry, the solutions to all problems start by drawing a line somewhere in the picture. I think that this is characteristic of my favorite kind of proof, where you can’t just move forward in a linear fashion to get to an answer, but you actually have to add something new, that you might not have thought was related to the question.

Most high school students already know far more about the binomial coefficients than they need to, and one of the things that they might know is the fact that if $k < \frac{n}{2}$, then  \binom{n}{k} \le \binom{n}{k+1}.