13 Point CircleDate: 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/ |
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