ABSTRACT
It has been shown that all of the standard compass-and-straightedge constructions of Euclidean geometry can be constructed using the original six axioms. In fact, working independently, Martin [25, pp. 145-159] showed that the operation equivalent to Huzita’s O6 (plus the definition of a point as a crease intersection) was, by itself, sufficient for the construction of all figures constructible by the full six axioms and that this included all compass-and-straightedge constructions. Conversely, Auckly and Cleveland [5,15], unaware of O5 and O6, showed that without O5 and O6 the field of numbers constructible by the other four HAs was smaller than the field of numbers constructible by compass and straightedge. An analysis of the hierarchy of fields that can be constructed using different axioms systems has been detailed [2, 4].
