# number of segments

• Jan 3rd 2013, 04:24 AM
rcs
number of segments
Problem:
there are 12 distinct named points on a line. How many segments can be named?

Is there a way or formula to know the number of segments can be named in a line with distinct points?

thanks
• Jan 3rd 2013, 04:40 AM
HallsofIvy
Re: number of segments
Is that the way you think mathematics is done- by plugging numbers into formulas? Where do you think those formulas come from?

Did you consider looking at simple cases? If there are no points, there is the single segment, (-infinity, infinity). If there is a single point, A, there are three segments, (-infinity, infinity), (A, infinity) and (-infinity, A). If there are two points, A and B, with A< B, there 6 segments, (-infinity, infinity), (-infinity, A), (-infinity, B), (A, B), (A, infinity), (B, infinity). Do you see a pattern? With n points you have the intervals from -infinity to each of the n points plus +infinity so n+1 such intervals. Then you have intervals from the "left most point" to each of the other points and to +infinity, n such intervals. That is, you have (n+1)+ (n)+ (n- 1)+ ... + 3+ 2+ 1. Do you know a formula for that? If not, can you work one out?
• Jan 3rd 2013, 04:59 AM
rcs
Re: number of segments
you write too much words in your reply but all those words are pointless :P
• Jan 3rd 2013, 05:14 AM
emakarov
Re: number of segments
Quote:

Originally Posted by rcs
you write too much words in your reply but all those words are pointless :P

Bravo! You win the grand prize for the most ungrateful response.
• Jan 3rd 2013, 07:34 AM
Plato
Re: number of segments
Quote:

Originally Posted by rcs
you write too much words in your reply but all those words are pointless :P

I agree that yours is not only rude in the extreme, it is not useful.

However, I disagree with Prof. Hals on the definition of line segment. In the Hilbert/Moore system of axiomatic geometry a line segment is defined as:
$\overline{PQ}=\{P,Q\}\cup\{X:P-X-Q\}$. The set of which is the union the set of two points with the set of all point between them. (see Moise)

So the answer to your question is $\binom{12}{2}$.
• Jan 3rd 2013, 07:48 AM
HallsofIvy
Re: number of segments
So you do not accept "infinite" line segments? I thought about that possibility.
• Jan 3rd 2013, 08:01 AM
Plato
Re: number of segments
Quote:

Originally Posted by HallsofIvy
So you do not accept "infinite" line segments? I thought about that possibility.

I can only speak for one set of axioms (I was a graduate assistant in several summer courses for in-service geometry teachers) based on RL Moore's notes.
The concepts of line, ray, half-lines are all different. Those are all what one may call "infinite". A line segment has two endpoints.
• Jan 4th 2013, 05:25 AM
rcs
Re: number of segments
Of course.... My mind is disturbed.... He made it more disturbed and insulted