1 you should read carefully what I wrote I did not say that get all algebraic numbers with the Huzita Hatori axioms for origami See for example Theorem 1 in One Two and Multi Fold Origami Axioms by Alperin and Lang In particular this is not original research 2 I asked you to discuss before making changes I think you should do it next time Note that it is not me who started this war 3 For the rest I gave the answers already I will wait couple of days and undo you changes I am 100 sure think this type of construction worth to be mentioned here