8 points are located on a circle. how many line segments can be drawn with these points as endpoints?
+26367 8 points are located on a circle. how many line segments can be drawn with these points as endpoints?
\(\begin{array}{|c|c|c|} \hline \text{Point } Number & \text{from Point} & \text{to Point} & \text{line number}\\ \hline 1 & 1 & 2 & 1\\ & 1 & 3 & 2\\ & 1 & 4 & 3\\ & 1 & 5 & 4\\ & 1 & 6 & 5\\ & 1 & 7 & 6\\ & 1 & 8 & 7\\ \hline 2\text{ new lines} & 2 & 3 & 8\\ & 2 & 4 & 9\\ & 2 & 5 & 10\\ & 2 & 6 & 11\\ & 2 & 7 & 12\\ & 2 & 8 & 13\\ \hline 3\text{ new lines} & 3 & 4 & 14\\ & 3 & 5 & 15\\ & 3 & 6 & 16\\ & 3 & 7 & 17\\ & 3 & 8 & 18\\ \hline 4\text{ new lines} & 4 & 5 & 19\\ & 4 & 6 & 20\\ & 4 & 7 & 21\\ & 4 & 8 & 22\\ \hline 5\text{ new lines} & 5 & 6 & 23\\ & 5 & 7 & 24\\ & 5 & 8 & 25\\ \hline 6\text{ new lines} & 6 & 7 & 26\\ & 6 & 8 & 27\\ \hline 7\text{ new line} & 7 & 8 & 28\\ \hline \end{array} \)
If we have 8 Points there are \(7 + 6 + 5 + 4 + 3 + 2 + 1 = \mathbf{28}\) line segments.
if we have n Points there are\(1 + 2 + 3+ 4 + 5 + \dots + (n-1) = \frac{ [ 1+(n-1) ] \cdot (n-1) } {2} = \mathbf{ \frac{ n\cdot (n-1) } {2} }\)line segments.
+26367 8 points are located on a circle. how many line segments can be drawn with these points as endpoints?
\(\begin{array}{|c|c|c|} \hline \text{Point } Number & \text{from Point} & \text{to Point} & \text{line number}\\ \hline 1 & 1 & 2 & 1\\ & 1 & 3 & 2\\ & 1 & 4 & 3\\ & 1 & 5 & 4\\ & 1 & 6 & 5\\ & 1 & 7 & 6\\ & 1 & 8 & 7\\ \hline 2\text{ new lines} & 2 & 3 & 8\\ & 2 & 4 & 9\\ & 2 & 5 & 10\\ & 2 & 6 & 11\\ & 2 & 7 & 12\\ & 2 & 8 & 13\\ \hline 3\text{ new lines} & 3 & 4 & 14\\ & 3 & 5 & 15\\ & 3 & 6 & 16\\ & 3 & 7 & 17\\ & 3 & 8 & 18\\ \hline 4\text{ new lines} & 4 & 5 & 19\\ & 4 & 6 & 20\\ & 4 & 7 & 21\\ & 4 & 8 & 22\\ \hline 5\text{ new lines} & 5 & 6 & 23\\ & 5 & 7 & 24\\ & 5 & 8 & 25\\ \hline 6\text{ new lines} & 6 & 7 & 26\\ & 6 & 8 & 27\\ \hline 7\text{ new line} & 7 & 8 & 28\\ \hline \end{array} \)
If we have 8 Points there are \(7 + 6 + 5 + 4 + 3 + 2 + 1 = \mathbf{28}\) line segments.
if we have n Points there are\(1 + 2 + 3+ 4 + 5 + \dots + (n-1) = \frac{ [ 1+(n-1) ] \cdot (n-1) } {2} = \mathbf{ \frac{ n\cdot (n-1) } {2} }\)line segments.
