Research Problem

Mathematics Research
First Research Problem

1. Problem:
Determining the number of line segments formed in connecting given numbers of points
Purpose:
To identify the number of lines produced in connecting the given points in a shorter way. To produce an easy equation for counting these lines.

2. Information available
A point is a position in space. Imagine touching a piece of paper with a sharp pencil or pen, without making any sideways movement. It has no size, but has a position. This means it has no volume, lenght and area. It is represented by a small 'X' or by a small dot (a small, round shape). In geometry, points are always labelled by capital letters (A,B,C...X,Y,Z).
A line segment is one of the basic terms in geometry. We may think of a line segment as a "straight" line that we might draw with a ruler on a piece of paper. A line segment does not extend forever, but has two distinct endpoints. We write the name of a line segment with endpoints A and B as "line segment AB" or as . Note how there are no arrow heads on the line over AB such as when we denote a line or a ray.
A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.

3. Data to be generated
Number of points: 1,2,3,4,5,6,7,8,9,10
Number of lines : 0,1,3,6,10,15,21,28,36,45

4. Availability of equipment
Mostly in Mathematics investigation materials or equipment are not necessary.