Dividing A Circle Into Thirds

"Andy Dingley" <[email protected]> wrote in message
news:[email protected]...
> On Fri, 28 Nov 2003 18:09:52 GMT, "Lawrence L'Hote" <[email protected]>
> wrote:

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

In article <[email protected]>,
>Rumpty <[email protected]> wrote:
>>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.

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

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


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"Rumpty" <[email protected]> wrote in message news:<[email protected]>...
>
> 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,

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

On Fri, 28 Nov 2003 10:02:09 -0500, "Rumpty"
<[email protected]> wrote:

>I need to divide a circle into thirds for a project I'm working on.

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.

>Suggestions? Oh, there is no center point to work with.

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

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


"Rumpty" <[email protected]> wrote in message
news:[email protected]...
> 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
>
> Radial Arm Saw Forum: http://forums.delphiforums.com/woodbutcher/start
>
> - - - - - - - - - - - - - - - - - - - - -
>
>
>
>

Scott Cramer wrote:
> On 28 Nov 2003, Rumpty spake unto rec.woodworking:
>
> > 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.
>
> 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.
>
>

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




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Scott Cramer wrote:
> On 28 Nov 2003, Rico spake unto rec.woodworking:
>
> > Scott Cramer wrote:
> >> On 28 Nov 2003, Rumpty spake unto rec.woodworking:
> >>
> >> > 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.
> >>
> >> 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.
> >>
> >>
> >
> > 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.
>
> 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.
>

Woops, right you are.


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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

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?

--

Rumpty

Radial Arm Saw Forum: http://forums.delphiforums.com/woodbutcher/start

- - - - - - - - - - - - - - - - - - - - -


"George Eversole Jr." <[email protected]> wrote in message
news:[email protected]...
> "Rumpty" <[email protected]> wrote in message
news:<[email protected]>...
> >
> > 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,
>
> 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

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


"Lawrence Wasserman" <[email protected]> wrote in message news:ntLxb.17
>
> Easy to find the centerpoint: draw in 2 chords, find midpoint, draw
> perpendiculars, they will intersect at the center.

"Andy Dingley" <[email protected]> wrote in message
news:[email protected]...
> On Fri, 28 Nov 2003 10:02:09 -0500, "Rumpty"
> <[email protected]> wrote:
>
> >I need to divide a circle into thirds for a project I'm working on.
>
> 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).

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

>I thought it was going to be the practical problem of positioning the point
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

Radial Arm Saw Forum: http://forums.delphiforums.com/woodbutcher/start

- - - - - - - - - - - - - - - - - - - - -


"Mark Jerde" <[email protected]> wrote in message
news:[email protected]...
> Lawrence L'Hote wrote:
> > "Andy Dingley" <[email protected]> wrote in message
> > news:[email protected]...
> >> On Fri, 28 Nov 2003 18:09:52 GMT, "Lawrence L'Hote"
> >> <[email protected]> wrote:
> >
> > Just a DOH! It's right. Brain fart.
> > Larry
>
> I thought it was going to be the practical problem of positioning the
point
> of the compass on an already cut out circle.
>
> -- Mark
>
>

On 28 Nov 2003, Rumpty spake unto rec.woodworking:

> 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.

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.

On 28 Nov 2003, Rico spake unto rec.woodworking:

> Scott Cramer wrote:
>> On 28 Nov 2003, Rumpty spake unto rec.woodworking:
>>
>> > 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.
>>
>> 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.
>>
>>
>
> 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.

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.

On Fri, 28 Nov 2003 10:02:09 -0500, "Rumpty"
<[email protected]> wrote:

>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.


Draw a circle with a compass. Set the compass on the edge of the
circle and draw an arc to cross the circle. Reset the compass at one
of the intersections and repeat. You'll get 6 equal sections of the
circle. Easy.

In article <4dNxb.338865$Tr4.1019538@attbi_s03>, [email protected] says...
>
> "Andy Dingley" <[email protected]> wrote in message
> news:[email protected]...
> > On Fri, 28 Nov 2003 18:09:52 GMT, "Lawrence L'Hote" <[email protected]>
> > wrote:
>
> Just a DOH! It's right. Brain fart.
> Larry
>
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?

In article <QbMxb.340489$Fm2.342680@attbi_s04>,
Lawrence L'Hote <[email protected]> wrote:
>
>"Andy Dingley" <[email protected]> wrote in message
>news:[email protected]...
>> On Fri, 28 Nov 2003 10:02:09 -0500, "Rumpty"
>> <[email protected]> wrote:
>>
>> >I need to divide a circle into thirds for a project I'm working on.
>>
>> 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).
>
>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
>
>

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.

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.

--
"If you are arrogant, who's going to care if you're the best?"

On Fri, 28 Nov 2003 18:09:52 GMT, "Lawrence L'Hote" <[email protected]>
wrote:

>Why is this method incorrect?

Go on then, enlighten us

Andy Dingley wrote:

> Strike an arc from the diameter on the circumference opposite your
> first point, just like the first arc you drew.

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

--
Michael McIntyre ---- Silvan <[email protected]>
Linux fanatic, and certified Geek; registered Linux user #243621
http://www.geocities.com/Paris/Rue/5407/

In article <[email protected]>,
Rumpty <[email protected]> wrote:
>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
>
>Radial Arm Saw Forum: http://forums.delphiforums.com/woodbutcher/start
>
>- - - - - - - - - - - - - - - - - - - - -
>


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
[email protected]

Lawrence L'Hote wrote:
> "Andy Dingley" <[email protected]> wrote in message
> news:[email protected]...
>> On Fri, 28 Nov 2003 18:09:52 GMT, "Lawrence L'Hote"
>> <[email protected]> wrote:
>
> Just a DOH! It's right. Brain fart.
> Larry

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

-- Mark