How quantum mechanics explains global warming - Lieven Scheire. Mercury Attacks Aluminum -amalgam. Lattice points visible from the origin « The Lumber Room. [A test of LaTeX-to-Wordpress conversion. Bugs remain, point them out. Original PDF] Here is a problem I love. It is simple to state, and it has a solution that is not trivial, but is easy to understand. The solution also goes through some beautiful parts, so I can promise it’s worth reading :-) [The solution is not mine. Question. Let us first imagine that we are standing at the origin, and that the grid is that of the lattice (integer) points. The blue points are visible; the grey points are not We now want to examine the question of which pairs are visible from the origin. Not visible? Is not visible because the point is "in the way", and the point obscures it.
Is not visible precisely when there is another lattice point blocking it, which is when there is an integer pair such that . Is not visible precisely when there is an integer dividing both and , and is visible when there is no such integer, i.e. when have no common factor. For this to happen, it must be the case that no prime number . Is . The Monty Hall Problem. Math animations - The story of PI.
How to theoretically turn a sphere inside out. When Will Time End? Sphere Inside out Part - II. How-to-imagine-the-tenth-dimension.