Points on a Circle:

Number of Chords for  n  Points
Number of Diagonals of an n-sided Polygon
Maximum Number of Regions Formed by the Circle and n Chords

Given a circle and points on the circle. With n points on the circle

1. What is the number of chords determined by n points?

2. What is the number of diagonals determined by n points?   See Triangular Numbers Problems, Problem 4.

3. What is the maximum number of regions determined by the chords and the circle rim.

See the image to the right, depiccting cases for 1 through 7 points.

NOTE:   Question 1 above is equivalent to the Handshake Problem (Problem 3):   Each  chord corresponds to a handshake between two people.

ALSO:  Since each chord corresponds to a pair of points, Question 1 is equivalent to finding the number of combinations of  n  things taken 2 at at time.

For Question 3, above, it might be useful to use colors in a systematic way to count the regions as the number of points increases.

Click HERE for a JavaGSP file to show building a table of values for each of the counts.

If JavaGSP does not work, click HERE for a GSP file and follow the directions on the page.




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