GeoGebra (version 2) provides 42 buttons, many of which have nothing to do with geometry. For example buttons control graphic manipulations (eg zoom in), construction steps and presentation (eg "Copy visual style"). Still others include "Delete", "Undo", "Redo" etc. Another classification which we choose to ignore concerns measurement, since this is not considered within Euclidean Constructions. These buttons are the following
| Measurement | Button |
|---|---|
| Distance | |
| Angle | |
| Polygon (area of) | |
| Relation between two objects | |
Associated with measurement there are a number of other buttons, which construct a "Segment with a given length from point" or an "angle with given size". These and vectors are also ignored. Notice that with these tools it is possible to measure a particular angle, a say with 
, and then using the button to construct a/3 effectively trisecting an angle using algebraic not geometric tools. This is not an Euclidean Construction.
Finally I omit what I term presentational forms of objects. For example, a semicircle is only part of a circle, as are circular arcs. While these are invaluable for focusing attention on parts of objects, they do not concern us here. It is worth noting that these presentational forms do have a bearing on the number of solutions when we ask for the intersection of two objects. If we take a circle and a non-tangential line via 
then there are either zero or two intersections. If we have a circle and ray 
then there could be zero, one or two intersections.
This leaves us with a number of purely geometrical buttons. The object of this paper is to identify the fewest possible with which all the others can be recreated. That is to say we try to identify a set of axiomatic buttons from which all the others can be constructed. If the functionality of another button can be constructed by axioms or previously constructed buttons then it is termed a theorem button. This provides at least one answer to the question in the title of the paper.
We shall first consider the following collection of buttons. These three have been chosen initially since they immediately provide one way to create all three of the classic identifiable objects in plane geometry, the line, circle and a conic section. Notice that the first two are special cases of the last. Hence, we should immediately be suspicious as to whether all are required. Is this truly a minimal set of axioms?
| Construction | Button |
|---|---|
| Line through two points | |
| Circle with center and through point. |  |
| Conic through five points |  |
In addition we may place a "New point" 
either unconstrained in space or to be constrained on one of these objects. We may also find the intersection of two objects 
and this button places new point(s) there. This latter operation applies to any two of line, circle and conic and it returns between zero and two new points, which are automatically assigned names. The intersection button is needed so that points can be created which are related to two existing objects. Without this, or something similar, there is no way to establish relationships between objects. Notice that implicit in identifying a point of intersection is an assumption of continuity.