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How do I divide a circle into 7 parts, Using a compass and without a protractor?I can...

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mack-n-vegas | eNotes Newbie

Posted June 29, 2011 at 7:13 AM via web

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How do I divide a circle into 7 parts, Using a compass and without a protractor?

I can do 2,3,4,6,12. I am an Artist not a Math Person. Thanks in advance.

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upstudent | Student, Grade 11 | eNotes Newbie

Posted June 29, 2011 at 12:59 PM (Answer #1)

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Hmm tricky question .divide it by using the scale pencil and applyin the log formula

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carey-ogola | Student, Undergraduate | eNoter

Posted July 21, 2011 at 7:23 PM (Answer #2)

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Draw the circle with its diameter AB.

Draw a line AC of length 14cm.

Divide AC into seven parts of 2cm each: AD, DE, EF, FG, GH, HJ, JC.

Draw a line joining point C to point B.

Using the set-square, draw line JJ’ parallel to line CB.

Draw a perpendicular to the diameter at point J’ such that the perpendicular cuts the circumference of the circle at point K.

Use the length CK to divide your circle into the required seven equal parts.

 

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harpmaker | Elementary School Teacher | eNotes Newbie

Posted December 26, 2011 at 10:02 AM (Answer #3)

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If you can divide a circle into 4 even wedges then you're half way to dividing it into 5.

Let's assume you've divided a circle into 4 even sections with a horizontal line and a vertical line. Bisect the top half of the vertical line (the line segment from the center of the circle to the top of the circle).  If you're not sure how to do this, the following is one method:

Set your compass to the radius of the circle, place its pivot where the vertical line crosses the top of the circle.  Draw an arc that crosses the circle in two places.  Draw a line between the points the arc intersects the circle - it will bisect the top half of the vertical line.

Put the pivot of the compass on the bisect point you just made.  Adjust the compass so that it reaches one of the points the horizontal line intersects the circle and draw an arc from it to the other intersection point between circle and horizontal line.

Put the pivot of the compass at the intersection of the arc you just drew and the vertical line it crossed.  Adjust the compass so that it can touch one of the points of intersection between the horizontal line and the circle.  The compass is now at the length of a secant that will divide the circle into five even sections just like the radius of a circle is the secant that divides the circle into six even sections. 

So now, just like divide a circle in to six sections, pick a point as the first of your 5, set the compass pivot there and mark intersection points clockwise and counterclockwise from it.  Using these two new points to start at, use the compass to make two more and there are your 5 evenly spaced points on the circle.  Draw line segments from these points to the center of the circle for 5 even wedges or extend the segments to the opposite side of the circle for ten wedges.

 

There is a drawing at the web site provided that does the same thing except it bisects one of the horizontal lines – the results are the same.  

You can now get a pretty good approximation for a dividing a circle into 9 or 11 parts.  On one piece of paper draw a circle and divide it into 10 sections – make sure the line segments that divide the circle extend past the circle a bit.  Now draw two more circles concentric with the original, divided one; make the first 10% larger and the second 10% smaller than the original. 

On a separate piece of paper draw a circle the same size as the one you divided into 10 parts.  The length between adjacent division lines where they intersect with the smaller concentric circle you drew on the other piece of paper are pretty close to the length of a secant that can be used to divide your fresh circle into 11 sections.  Conversely the adjacent intersections from the larger circle will give you a good first try at dividing a circle of the original size into 9 sections.    

There’s also a geometric method (done with compass and straightedge only) for approximating dividing a circle into seven even wedges, but it has slipped my mind and I haven’t been able to find my notes on it either.

Sources:

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mikesters | eNotes Newbie

Posted March 18, 2012 at 6:19 AM (Answer #4)

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you can't really do that, see
http://www.cut-the-knot.org/Curriculum/Geometry/NCircleParts.shtml#solution

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