# Dividing A Circle Into Thirds

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• posted on November 28, 2003, 3:02 pm
I need to divide a circle into thirds for a project I'm working on. Geometry was 30 years ago and I can't find my old book.
Suggestions? Oh, there is no center point to work with.
--
Rumpty

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• posted on November 28, 2003, 3:32 pm
Using a Protractor find the center of the circle and create a Line (radius) then use 120 degrees. A circle is 360 degrees divided by 3 = 120 degrees.
Rich

Geometry
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• posted on November 28, 2003, 3:53 pm
On 28 Nov 2003, Rumpty spake unto rec.woodworking:

Measure the circle's diameter. Set your compass or dividers to 1/2 the diameter. Step off divisions around the circle. If you were accurate, you'll have six equal steps; if not, adjust until you do.
Connect opposite pairs of points to find the center, then draw every other radius to make thirds.
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• posted on November 28, 2003, 8:07 pm
Scott Cramer wrote:

As in your method: Measure the circle's diameter. Set your compass or dividers to 1/2 the diameter. Step off divisions around the circle.
Then starting at the same point again, step off divisions going around the circle in the opposite direction.
If you were reasonably close, the two sets of 6 marks will be quite close to each other. The correct points are 1/2 way between each pair of marks.
Rico
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• posted on November 28, 2003, 9:00 pm
On 28 Nov 2003, Rico spake unto rec.woodworking:

That is only true for the pair of points opposite the starting point. The points closest to the starting are off by 1/6th of the error, and the other two points are off by 1/3rd of the error.
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• posted on November 28, 2003, 10:49 pm
Scott Cramer wrote:

Woops, right you are.
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• posted on November 28, 2003, 4:25 pm
On Fri, 28 Nov 2003 10:02:09 -0500, "Rumpty"
If you know the radius, this is easy with a pair of dividers. Step them around the circumference. They'll mark out 6 points and should end up exactly where you began (if they don't, they weren't set to the exact radius). Just use 3 of these points.

If you don't already know the radius, find the centre point and then use it to set the dividers accurately to the radius.
To find the centre point, use the dividers. Set them to roughly 3/4 of the diameter and pick a point on the circumference. Mark out two points on the circumference from this, with an arc between them. Now place the dividers on each of these points in turn and strike arcs roughly opposite the first point, through the circumference. Draw a line (a diameter) from the first point, to the intersection of these two arcs.
Now bisect the diameter. Strike an arc from the diameter on the circumference opposite your first point, just like the first arc you drew. These two arcs should now intersect at two points. Connect these two points with a straight line that should pass through the diameter at the centre of the circle, and at right angles to the diameter. -- Die Gotterspammerung - Junkmail of the Gods
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• posted on November 28, 2003, 6:09 pm
wrote:

Ummmm doesn't work...but a good approximation. Try this. Get out your handy drawing compass and draw a circle. Now use the method described above w/o changing the compass setting(compass is set at the radius of the circle). Why is this method incorrect? The solution is left to the student. Larry
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• posted on November 28, 2003, 7:05 pm
wrote:

Go on then, enlighten us
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• posted on November 28, 2003, 7:19 pm

Just a DOH! It's right. Brain fart. Larry
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• posted on November 28, 2003, 7:33 pm
Lawrence L'Hote wrote:

I thought it was going to be the practical problem of positioning the point of the compass on an already cut out circle.
-- Mark
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• posted on November 28, 2003, 7:47 pm
If you have a 30/60/90 drafting guide it is easy. Set the 30/90 edge on a line through the center of the circle and mark the intersection of the 30/60 line where it contacts the circumference at both sides. Flip it and repeat, being sure the pointy end is still on one of the marks. You have defined an equilateral triangle inside the circle thus trisecting it when you draw a line to the center from the points
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• posted on November 28, 2003, 9:34 pm

of the compass on an already cut out circle.
No, actually it's the need to drill out a "Snapper" snowblower driven wheel to fit a "Homelite" snowblower mounting holes, there ain't no center reference, and there ain't no more OEM or aftermarket parts to fit this snow blower since Homlite sold the line to John Deere who sold the line to some Japanese company...
--
Rumpty

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• posted on November 29, 2003, 6:01 am

how about creating a center point by making a pattern: cut a plywood circle and mount some dowel rod to simulate the Snapper hub and studs it wants. this will center the plywood circle on the snapper wheel.
on the side of the plywood where the dowels do not project, find the center of the circle and use the equalteral triangle method to define the division into thirds. mark off the homelite stud locations, transfer, and drill. -ghe
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• posted on November 29, 2003, 2:34 pm
I ended up machining an aluminum mandrel that would center both wheels, i.e. 2" with a 1" shoulder, this allowed using a transfer punch to mark the new mounting holes. It worked well.
So how do you divide up a trapezoid into 13 parts?
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Rumpty

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• posted on November 29, 2003, 5:35 pm

Don't feel bad. I was going to complain as well, but I looked up the formula for the chord of a circle first :-).
--
Where ARE those Iraqi WMDs?

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• posted on November 29, 2003, 3:52 pm

It is -provably- *PRECISELY**CORRECT*.
strike a circle, radius OA ('O' is the center, 'A' is on the circle) strike an arc, of the same radius, centered at 'A', intersecting the circle at 'B'
_by_definition_, 0A, and 0B are the same length, each being a radius of the circle. AB was constructed as the same length as OA.
THEREFORE, 0AB is an *equilateral*triangle*. and all the angles are *precisely* 60 degrees.
Repeating the process around the circle will lead to _exactly_ *six* such equilateral triangles, which *precisely* fill the entire 360 degrees of the circle.
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• posted on November 29, 2003, 2:41 am
Andy Dingley wrote:

Wow, I gotta get some dividers. Sounds a lot more precise than eyeballin' it.
--
Michael McIntyre ---- Silvan < snipped-for-privacy@users.sourceforge.net>
Linux fanatic, and certified Geek; registered Linux user #243621
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• posted on November 30, 2003, 5:22 am
Andy Dingley provided one (good) method of finding the center of a circle...
Here's a method I often use, which is a tad simpler:
Place the point of a compass (or dividers) on the original circle A somewhere, and make a new circle B. If you can, make circle B just a little bigger than A, but the size really isn't important.
Draw two more circles, C and D, the same size as B. Place C's center on one of the intersections of A & B. Place D's on the other. Note that C and D both will intersect A at B's center.
Now draw a line through the two intersections of B and C, and another line through the two intersections of B and D. The two lines intersect at the center of A.
This is much easier to do than to describe. Only takes a few seconds. When you see how the elements fall together, you will realize that you don't need whole circles. Short arcs in the appropriate places suffice.
Jim
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• posted on November 28, 2003, 5:20 pm

Easy to find the centerpoint: draw in 2 chords, find midpoint, draw perpendiculars, they will intersect at the center. Now set your dividers to the radius, then step off that length around the circumference. If you're accurate you should land on the first point again at the 5th step-off. Each adjacent set of points will be 60 degrees further along the circumference, so use every other point & the center to divide into thirds.
--

Larry Wasserman Baltimore, Maryland