1. ## cyclically ordered set

A polygon is a geometric object consisting of anumber of points, vertices, and an equal number of line segments, sides, namelya cyclically ordered set of points in a plane, with no three successive pointscollinear, together with the line segments joining consecutive pairs of the points.
What is cyclically ordered set of point?
Are solid bodies have cyclically ordered set of point?

2. ## Re: cyclically ordered set

The title is reading comprehension ... for this message.
What it the cyclically ordered set of points in other word?!

3. ## Re: cyclically ordered set

Originally Posted by policer
The title is reading comprehension ... for this message.
What it the cyclically ordered set of points in other word?!
Given your lack of proficiency in English this link may be useless.

4. ## Re: cyclically ordered set

I can see why every polygon has cyclic set.
But there is a proof that every polygon has cyclic set?
I know that polygon in my bad English : A "zigzag" line or maybe the term is broken line... that not pass throw itself (intercept himself) and create a closed figure (that the starting point is the ending point of broken line). Because of that it is obvious why every polygon has cyclic set.
(1)Can somebody phrase in better English the underlined text?
(2)There is a proof or because of the definition every polygon has [(maybe "have" is the word?)] cyclic set?

5. ## Re: cyclically ordered set

Originally Posted by policer
I can see why every polygon has cyclic set.
But there is a proof that every polygon has cyclic set?
I know that polygon in my bad English : A "zigzag" line or maybe the term is broken line... that not pass throw itself (intercept himself) and create a closed figure (that the starting point is the ending point of broken line). Because of that it is obvious why every polygon has cyclic set.
(1)Can somebody phrase in better English the underlined text?
(2)There is a proof or because of the definition every polygon has [(maybe "have" is the word?)] cyclic set?
It sounds to me like Plato has the right idea. However there is nothing that prevents us from just taking a finite number of points and linking them together. Labeling the points $\displaystyle p_i$ we can write a function that goes from point to point. For example $\displaystyle f(p_1) = p_2$, $\displaystyle f(p_2) = p_3$ etc. until we get to the last point $\displaystyle f(p_n) = p_1$, at which point it starts over again. Is this the kind of thing you are talking about?

-Dan