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Imagine a Tic-Tac-Toe grid. I.e., a square that is subdivided into 3 times 3 equal 9 smaller squares in which you can play a game. If you look at it straight, it looks like this. If you look at it from an angle, it gets perspectively distorted. This also happens when you take a photo of it or when you make a drawing. Now, imagine, in such a drawing, you only have the outline given. How can you construct the rest of the grid? And, in particular, can you do it in a way that generalizes to other subdivisons like 4 by 4 or 5 by 5? Im Bernhard Werner and this is an introduction to Projective Geometry via Tic-Tac-Toe grids. Projective Geometry is a field of mathematics that is interested in how various concepts from Euclidean Geometry can be generalized. Euclidean Geometry is the type of geometry you learn in school: points, lines, distances, angles, circles, etc. But distances, for example, do not get preserved under perspective distortions. We can see that with the image of the Tic-Tac-To
