It’s impossible because of the rules of the game. Euclidian geometry doesn’t allow for straight edges of defined lengths or with pre-set marks, which makes a lot of things impossible. If you allow for different rules, like for example special rulers, or the ability to fold the paper, trisecting an angle becomes possible
As to the natural question of why we care about Euclidian geometry so much then, it’s got very simple rules and a lot you can do with them.
Comments
It’s impossible because of the rules of the game. Euclidian geometry doesn’t allow for straight edges of defined lengths or with pre-set marks, which makes a lot of things impossible. If you allow for different rules, like for example special rulers, or the ability to fold the paper, trisecting an angle becomes possible
As to the natural question of why we care about Euclidian geometry so much then, it’s got very simple rules and a lot you can do with them.