What is a tilted square?

A tilted square, as explained by Steven Strogatz in the podcast "The Knowledge Project", is essentially a diamond shape resulting from a thought experiment in non-Euclidean geometry. Instead of being the typical square with sides parallel to the x and y axes, this "square" appears rotated, resembling a tilted, or diamond-like shape on its side. This visualization challenges the traditional notion of geometric shapes like circles and squares as being purely round or having parallel and perpendicular sides respectively. It encourages thinking about geometric figures in different contexts and rules, essentially pushing the boundaries of traditional Euclidean geometry 1.