What does this prove Some of the most gorgeous visual shrink proofs ever invented

Bit of a mystery Mathologer today with the title of the video not giving away much. Anyway it all starts with the quest for equilateral triangles in square grids and by the end of it we find ourselves once more in the realms of irrationality. This video contains some extra gorgeous visual proofs that hardly anybody seems to know about. 0:00 Intro 0:47 First puzzle 2:24 Second puzzle 3:50 Edward Lucas 4:41 Equilateral triangles 13:15 3d 3rd puzzle 19:52 30 45 60 29:31 Credits Here are links to, references of some of the things I mention in the video: Joel Hamkin s blog posts that inspired this video: There is also a whole chapter about all this and much more related maths in his new book Here is another really good article which includes a nice characterisation of the triangles that can be found in