Geometry Construction

[atvfan]

I am stuck. I am working on a geometry problem that has me stumped.

You are given an integer greater than one and LN is a line segment.

Why can a regular polygon with 2(n) sides centered at S with the segment LN as a radius be constructed, if and only if, a regular polygon with n sides centered at S with the segment LN as a radius be constructed?

 

[Deleted member 4993]

I am stuck. I am working on a geometry problem that has me stumped.

You are given an integer greater than one and LN is a line segment.

Why can a regular polygon with 2(n) sides centered at S with the segment LN as a radius be constructed, if and only if, a regular polygon with n sides centered at S with the segment LN as a radius be constructed?

And what are your thoughts/efforts/work???

What does your book say??

class notes??

 

[Pklarreich]

Let's reword the question:

Suppose you have a R.P. of, say, 7 sides. How would you turn it into a R.P. of 14 sides with the same radius?

Suppose you have a R.P. of, say, 18 sides. How would you turn it into a R.P. of 9 sides with the same radius?

Would the answers to these questions take care of things?

 

[atvfan]

To turn a reg polygon with 7 into 14.
First, bisect the side. This will tell you where the point on the edge of the polygon should be located.

Next, you need to determine how far out from the polygon the new vertex should be located so that the sides will all be congruent.

Choosing the point outside the polygon I am not sure about. Can it be arbitrary or does it need to be a certain distance from the original side?

Thanks