Compass-and-straightedge construction (aka Euclidean construction) is a method of drawing precise geometric figures using only a compass and a straightedge (like a ruler without the markings). MathOpenRef maintains a catalog of many common constructions, each with an explanatory animation and a proof. This YouTube video demonstrates how to construct almost every polygon that can be constructed using these methods. [more inside]
Geogebra is an interactive geometry tool which started as a free clone of Geometer's Sketchpad, but is now also an algebra, statistics and calculus tool. It is available for download for Windows, Mac, Linux, iOS and Android, or as a web app. [more inside]
The nightmare corpse-city of R'lyeh was built in measureless eons behind history by the vast, loathsome shapes that seeped down from the dark stars.
Have you ever wondered what non-euclidean geometry actually looks like? This video uses a custom ray tracer for the Minecraft engine to give some examples.
A fun flash rhythm builder based on Euclidean patterns. For those who enjoyed Circuli (previously) and the Whitney Music Box (also previously), I recommend Wouter Hisschenmoller's rhythm builder, which uses a Euclidean algorithm to create African-like rhythms, which you can layer to create some fun and complex beats.