Associated Topics || Dr. Math Home || Search Dr. Math

### 13 Point Circle

```
Date: 8/26/96 at 16:45:43
From: Anonymous
Subject: 5 and 13 point circles

Mr. Fessenden's 8th grade class asks, "Is there an easy way to find
out how many lines it takes to connect every point on a 13 point
circle with every other point on the circle? Several students have
tried to find a pattern or a shape to fit. Some drew lines to the
center and tried to find a pattern. We would like to know if there is
an easier way to figure out this puzzle.
```

```
Date: 8/30/96 at 16:4:45
From: Doctor Ceeks
Subject: Re: 5 and 13 point circles

Hi,

We can observe that no line intersects a circle in more than 2 points.
Therefore, for thirteen points, it is necessary that at least 7 lines
be used, for 6 lines can only carry at most 12 of the points and there
will be a thirteenth point left out.

Next, notice that it's always possible to solve the problem using 7
lines.  One simply pairs up points with lines until 12 points are on
lines, and then, through the thirteenth point, draw a line not
parallel to any of the 6 already drawn lines.

This argument works for any odd number of points.

For an even number, say 2M, of points, it is true that you can do it
with M lines.

-Doctor Ceeks,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Conic Sections/Circles
Middle School Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search