When you explained why the 1 x 1 = c^2 isosceles triangle is important to know it blew my mind. In fact this whole lesson really opened my eyes to the power behind math. I was always good at solving problems but never the understanding behind everything. I had a hard time with proofs when in reality it was just because I wasn’t trying to learn why things work the way they do. I just wanted to solve the problem and go play video games xD.
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Glad you found this lecture helpful @Kevin-Brandon, and apologies for only just responding - I totally missed your post.
Math is full of these little tricks and insights, so it’s often good to think about why things behave a certain way.
In this case of a 1-1-root2 triangle, you can take this base case and use something like float diagonalMoveDistance = gridSize * Math.sqrt(2) to move diagonally along a grid in your game.
Then if you change your grid size the new diagonal movement distance will fix itself without you ever having to worry about it.
Personally, I really like the geometric proof of the Pythagorean theorem so I had to include it in the lecture. Proofs can often be quite dull but I love it when they can be solved in a nice visual way like this.