Maths Project, Euclidean Geometry

arvenkenobi
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1. Maths project to investigate compass and straightedge constructions



2. Most of the project is fine, but i need to find out the mimimum number of constructions to bisect an angle, a line segment, etc.



3. I can prove that you can bisect an angle, and it requires 4 steps to do it. But no idea how to prove the minimal no. of steps. please help!
 
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Any help would be greatly appreciated!
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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