Proof without words of the two-color case of Ramsey’s theorem. (Credit: CMG Lee, Wikimedia) Generally when assuming a chaotic (i.e. random) system like an undirected graph, we assume that if we start coloring these (i.e. assign values) with two colors no real pattern emerges. Yet it’s been proven that if you have a graph with […]
Ah, tiles. You can get square ones, and do a grid, or you can get fancier shapes and do something altogether more complex. By and large though, whatever pattern you choose, it will normally end up repeating on some scale or other. That is, unless you go with something like a Penrose Wave Tile. Discovered […]
If you’re like us, you’ve studied the mathematician [Euler], but all you really remember is that you pronounce his name like “oiler” and not much else. [Welch Labs], on the other hand, not only remembers what he learned about logarithms and imaginary numbers but also has a beautiful video with helpful 3D graphics to explain […]
You’ve probably used Wolfram Alpha and maybe even used the company’s desktop software for high-powered math such as Mathematica. One of the interesting things about all of Wolfram’s mathematics software is that it shares a common core engine — the Wolfram Engine. As of this month, the company is allowing free use of the engine […]