This is a quick note about straightedge and compass constructions, in relation to my set.
A quick definition: a straightedge is an arbitrarily long straight edge, and a compass is a circle drawing tool. Specifically, with a straight edge you can:
Pick any two lines and draw the line through them
Pick a point and draw a line through it
Draw an arbitrary line
And with a compass you can:
Pick two points, \(A,B\) and draw a circle centered at \(A\) with radius \(|AB|\)
Pick a point and draw a circle centered at that point
Draw an arbitrary circle going through a point
Draw an arbitrary circle
Just a quick note about a compass, assume in the questions that you are using a non-collapsing compass, that is, if you draw a circle then you can make your next circle have the same radius as the circle you constructed free of charge.
I'll call a geometric construction constructible if it can be constructed with a straightedge and compass. For example
which shows that an equilateral triangle is constructible.
A constructible number, say \(x\), is defined as follows:
If given a unit length, it is possible to construct a segment of length \(x\).
Also a shape is constructible given another shape if it is possible to construct another shape given the first one. So although a \(22\)-gon is not constructible, it is constructible given an \(11\)-gon.
Lastly a use is a single use of a compass or straightedge, as defined above. So the equilateral triangle takes 5 moves.
Again this is in relation to my set.