Security through obscurity doesn't work. Every once in a while I like to prove this fact, by getting worldwide high scores on vulnerable leaderboards. The first time I did this was to Area Flat 3 (which was an awesome game when I was in elementary school, and is still pretty fun). Check the all-time top 100 scores for H4X0R (I know, not very original; I was 13, sue me). But that hack was child's play compared to this one. Continue reading Righteous hack: getting 263 - 1 points in a silly Facebook game
Although a closed form solution exists for the roots of polynomials of degree ≤ 4, the general formulae for cubics (and quartics) is ugly. Various simplifications can be made; commonly, the cubic \(a_3\,x^3+a_2\,x^2+a_1\,x+a_0\) is transformed by substituting \(x = t-a_2/3a_3\), giving Continue reading Solving Cubic Polynomials
A well known (if not by name) theorem is the Abel–Ruffini theorem, which states that there is no algebraic expression for the roots of polynomials with degree higher than 4.
A not-so-well-known fact is that for any polynomial \(P(x)\), it is possible to find (with exact arithmetic) a set of ranges each containing exactly one root of \(P(x)\). One such algorithm is due to James Victor Uspensky in 1948. Continue reading Solving Polynomials
Hell is freezing over. Or something. This month I've created a twitter and now a blog-type thing here. Welcome to 2006, I know.