Dividing A Circle Into Thirds

[Rumpty]

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.

[RKON]

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

[Scott Cramer]

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.

[Andy Dingley]

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

[Lawrence Wasserman]

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.

[Lawrence L'Hote]

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

[Andy Dingley]

Go on then, enlighten us

[Lawrence L'Hote]

Just a DOH! It's right. Brain fart. Larry

[Mark Jerde]

I thought it was going to be the practical problem of positioning the point of the compass on an already cut out circle.

-- Mark

[Greg]

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

[Rico]

No need to chase your tail finding the exact radius.

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

[Scott Cramer]

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.

[Wood Butcher]

That will work, but it's too much work.

Get a plastic drafting triangle. Place it over the circle with the 90° corner on the circumference. Mark the points where the 2 adjacent sides cross the circumference. Connect these 2 points - this line is a diameter. Repeat the above to establish another diameter line. The 2 diameter lines will intersect at the center of the circle.

Art

[Rumpty]

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...

[Rico]

Woops, right you are.

[Larry Jaques]

How about D + 1rch? It's not scientific, but it's close!

(No, that doesn't mean "rarified carbon hashmark".)

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[Silvan]

Wow, I gotta get some dividers. Sounds a lot more precise than eyeballin' it.

[George Eversole Jr.]

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

[mel]

lay your circle onto a piece of square stock like plywood with the edges flush with one side and the adjacent 90 degree side. Take a framing square and butt it to the opposite side scribe a line. measure from edge to line and divide by 2 and you have your radius. use this measurement to divide your square into 4ths. 2x2 smaller squares. use center point and a compass and draw a smaller circle in center. draw a straight line where circle intersects lines, measure and divide these lines into 3rds. from center point to each third point of line is 1/12th of your circle. 4 of these =1/3.

[Rumpty]

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?