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.

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