Large prime numbers

As of this writing, the largest known prime number is 277232917-1. “Not large enough!”, I say. Let’s write a computer program that will print out a larger prime number. No, not a program that will take billions of years to run. It should take only a few minutes. There is a small catch. Hardly worth……

Summary of some Win32 I/O character encoding behavior

This post is about programming a Windows Win32 application, mainly one that uses the console (command line). It summarizes the results of some tests I performed. Maybe you ported a Unix utility to Windows, but you find that it doesn’t work with filenames that contain Japanese characters. This information may help, though specific recommendations will……

When will Eris be closer than Pluto?

The dwarf planet Eris is sometimes closer to Earth than Pluto is. That’s no secret. Wikipedia’s article on Eris even has a chart similar to the one below. But I feel like this fact has been strangely ignored in the whole is-Pluto-a-planet debate. Eris is a tiny bit smaller in diameter than Pluto, though it’s……

How to draw an elliptical orbit

Maybe you’ve heard of the Milankovitch cycles, one of which involves changes to the eccentricity of the Earth’s orbit, as it is perturbed by other objects in the Solar System. Suppose you want to depict this with a diagram, using a circle, and an ellipse of exaggerated eccentricity. You could just draw any old random……

The observable universe

[I suggest reading my earlier post, The Big Bang, before this one.] The observable universe (OU) is the part of the universe that we can, at least in principle, observe, from a designated vantage point at a given place and time. This post is my attempt to figure out in more detail exactly what the OU……

A puzzle about a Fibonacci-like sequence

I’m thinking of a mathematical sequence, $latex S$, whose terms are all nonnegative real numbers. It is infinite in both directions. Like the Fibonacci sequence, it satisfies the relation: $latex \displaystyle S_n=S_{n-1}+S_{n-2}$ And we are given: $latex \displaystyle S_0=1$ What is the value of $latex S_1$? Surprisingly, you have enough information to figure it out. Note……

The Big Bang

In cosmology, the term the Big Bang has several subtly different meanings. It means the moment in time, it means the “explosion” event, and it means the all the events and states of the early universe. How early is early? Could be lots of things. Maybe just the first fraction of a second, maybe the……