The first four axioms with two given points define a system weaker than compass and straightedge constructions: every shape that can be folded with those axioms can be constructed with compass and straightedge, but some things can be constructed by compass and straightedge that cannot be folded with those axioms. The numbers that can be constructed are called the origami or pythagorean numbers, if the distance between the two given points is 1 then the constructible points are all of the form formula_24 where formula_25 and formula_26 are Pythagorean numbers. The Pythagorean numbers are given by the smallest field containing the rational numbers and formula_27 whenever formula_25 is such a number.